{"label":"34.4.a","level":34,"weight":4,"dims":{"new":4,"cusp":12,"eisenstein":4,"modsym":28},"old":[[17,4,2]],"T":[[3,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 17, 34]: [1, 2, 6, 16] (certified at ell = 2147483489)","T = [(3, 1), (5, 1)]; h of degree 4 = 1 x 4 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"34.4.a.a","letter":"a","dim":1,"charpoly":["20","1"],"traces":["1","-2","-2","4","-18","4","-10","-8","-23","36","-6","-8","74","20","36","16","17","46","-88","-72","20","12","-114","16","199","-148","100","-40","-90","-72","-310","-32","12","-34","180","-92","86","176","-148","144","90","-40","368","-24","414","228","-384","-32","-243","-398","-34","296","-258","-200","108","80","176","180","240","144","302","620","230","64","-1332","-24","-964","68","228","-360","-390","184","722","-172","-398","-352","60","296","-898","-288","421","-180","912","80","-306","-736","180","48","1446","-828","-740","-456","620","768","1584","64","-1438","486","138","796","258","68","1400","-592","-360","516","1662","400","-1114","-216","-172","-160","-54","-352","2052","-360","-1702","-480","-170","-288","-1295","-604","-180","-1240","-1332","-460","-748","-128","-736","2664","-354","48","880","1928","-1800","-136","-426","-456","-1090","720","768","780","-444","-368","1620","-1444","486","344","-1938","796","-748","704","-391","-120","5580","-592","-922","1796","516","576","1140","-842","-1222","360","-216","-1824","-4062","-160","3279","612","2024","1472","3990","-360","-1990","-96","-480","-2892","912","1656","-418","1480","-604","912","-1548","-1240","-102","-1536","-1000","-3168","-2400","-128","-1702","2876","2664","-972","54","-276","3818","-1592","1928","-516","900","-136","-1620","-2800","2622","1184","528","720","-2374","-1032","780","-3324","-6624","-800","3100","2228","-1444","432","1258","344","-2140","320","-4577","108","2322","704","1082","-4104","-120","720","-534","3404","6912","960","1796","340","-4680","576","3530","2590","-3542","1208","4374","360","-6512","2480","-1824","2664","-1188","920","684","1496","612","256","-1914","1472","-860","-5328","2070","708","1356","-96","4644","-1760","-2892","-3856","-546","3600","5144","272","1480","852","-1194","912","1286","2180","7130","-1440","-678","-1536","-5302","-1560","-3168","888","-900","736","289","-3240","2876","2888","-6882","-972","-4320","-688","-600","3876","-8436","-1592","-3680","1496","-516","-1408","-5436","782","1892","240","-2800","-11160","5226","1184","2714","1844","-4140","-3592","150","-1032","540","-1152","-3324","-2280","-1496","1684","14726","2444","2228","-720","3840","432","992","3648","-1978","8124","17352","320","5186","-6558","108","-1224","1860","-4048","5860","-2944","-4104","-7980","-1110","720","3062","3980","7400","192","-4974","960","7020","5784","340","-1824","-8052","-3312","885","836","2590","-2960","-12996","1208","-7570","-1824","-2070","3096","2580","2480","4178","204","2664","3072","-6660","2000","3110","6336","1496","4800","-1356","256","-1080","3404","-8464","-5752","-5190","-5328","-1938","1944","708","-108","16164","552","-5074","-7636","-1760","3184","13290","-3856","-22940","1032","-7578","-1800","-516","272","-15574","3240","852","5600","-2400","-5244","-16416","-2368","2180","-1056","9930","-1440","14450","4748","8832","2064","3383","-1560","-3020","6648","888","13248","1854","1600","-6970","-6200","-3240","-4456","10032","2888","-2086","-864","5589","-2516","420","-688","-26028","4280","3876","-640","-10254","9154","-540","-216","1496","-4644","13320","-1408","10046","-2164","1700","8208","-16650","240","8408","-1440","-11160","1068","17712","-6808","9640","-13824","1844","-1920","-2208","-3592","-17512","-680","5934","9360","16002","-1152","6364","-7060","-2280","-5180","25884","7084","11846","-2416","2444","-8748","-5568","-720","-1530","13024","-2484","-4960","3900","3648","14258","-5328","8124","2376","4734","-1840","-4644","-1368","-6558","-2992","-17658","-1224","-7220","-512","-8800","3828","-25200","-2944","2304","1720","-7980","10656","17898","-4140","-2068","-1416","3980","-2712","-5270","192","829","-9288","-5520","3520","6660","5784","-29916","7712","-1824","1092","1458","-7200","-394","-10288","836","-544","20052","-2960","1286","-1704","-6946","2388","7920","-1824","8980","-2572","3096","-4360","-20118","-14260","27232","2880","204","1356","-15504","3072","972","10604","-4210","3120","-2694","6336","-25150","-1776","4800","1800","-22686","-1472","2222","-578","3404","6480","-9120","-5752","1548","-5776","30636","13764","-11688","1944","27280","8640","-108","1376","-15774","1200","3060","-7752","-7636","16872","13632","3184","-2062","7360","22172","-2992","23310","1032","7586","2816","-1800","10872","-28416","-1564","-1666","-3784","3240","-480","11802","5600","-9574","22320","-11400","-10452","-14460","-2368","-899","-5428","-1056","-3688","1462","8280","6668","7184","4748","-300","13464","2064","-17982","-1080","8970","2304","-21102","6648","4718","4560","13248","2992","-96","-3368","-1440","-29452","-6200","-4888","6270","-4456","6372","1440","-16606","-7680","-2004","-864","-30466","-1984","-2516","-7296","-15840","3956","10260","-16248","4280","-34704","-1812","-640","10370","-10372","19900","13116","17262","-216","14380","2448","-4644","-3720","-13650","8096","7668","-11720","-2164","5888","-19092","8208","-21286","15960","-1380","2220","19620","-1440","1530","-6124","1068","-7960","138","-14800","-7568","-384","-13824","9948","-2580","-1920","-11338","-14040","20654","-11568","35340","-680","7992","3648","9360","16104","-20238","6624","-14000","-1770","-7060","-1672","-17910","-5180","25112","5920","-4283","25992","6256","-2416","31478","15140","-8748","3648","5784","4140","21776","-6192","13024","-5160","28482","-4960","34884","-8356","-20976","-408","-16620","-5328","-12694","-6144","2376","13320","13464","-4000","-18310","-6220","-1368","-12672","-12426","-2992","11140","-9600","7038","2712","17760","-512","-19042","2160","3828","-6808","-198","16928","-61690","11504","1720","10380","-7920","10656","2340","3876","-9000","-3888","16596","-1416","18566","216","-2712","-32328","540","-1104","22348","10148","-9288","15272","19638","3520","-6528","-6368","-33258","-26580","-4332","7712","-20520","45880","1092","-2064","-29310","15156","19598","3600","-10288","1032","21996","-544","-32384","31148","17020","-6480","39438","-1704","-30922","-11200","2388","4800","-1614","10488","-20698","32832","-2572","4736","-4131","-4360","73116","2112","-31000","-19860","-34866","2880","-16289","-28900","1356","-9496","-59022","-17664","12950","-4128","10604","-6766","-9804","3120","34430","6040","-36432","-13296","23226","-1776","32912","-26496","1800","-3708","-7704","-3200","-71820","13940","-578","12400","5388","6480","-71336","8912","33074","-20064","13320","-5776","-15370","4172","13764","1728","-16542","-11178","30332","5032","8640","-840","14322","1376","7480","52056","-2526","-8560","33792","-7752","-16416","1280","16872","20508","27900","-18308","-4386","1080","7360","432","7524","-2992","41114","9288","-5934","-26640","19398","2816","-5472","-20092","10872","4328","3540","-3400","17696","-16416","-3784","33300","-28860","-480","17114","-16816","-32200","2880","-9846","22320","21384","-2136","-10452","-35424","1836","13616","15962","-19280","-5428","27648","-30570","-3688","-10260","3840","18000","4416","-23178","7184","53428","35024","-300","1360","5718","-11868","43200","-18720","-1080","-32004","4260","2304","66309","-12728","-38226","14120","30636","4560","22988","10360","2992","-51768","4392","-14168","10900","-23692","-29452","4832","60786","-4888","-8676","17496","25622","11136","-38550","1440","-972","3060","-7680","-26048","-41952","4968","18866","9920","-1984","-7800","-68724","-7296","-38554","-28516","8600","10656"]},{"label":"34.4.a.b","letter":"b","dim":1,"charpoly":["-14","1"],"traces":["1","-2","-2","4","16","4","24","-8","-23","-32","62","-8","-62","-48","-32","16","-17","46","-20","64","-48","-124","-12","16","131","124","100","96","80","64","-208","-32","-124","34","384","-92","-356","40","124","-128","22","96","-312","248","-368","24","24","-32","233","-262","34","-248","-462","-200","992","-192","40","-160","240","-128","812","416","-552","64","-992","248","-216","-68","24","-768","732","184","178","712","-262","-80","1488","-248","700","256","421","-44","-992","-192","-272","624","-160","-496","-390","736","-1488","-48","416","-48","-320","64","-146","-466","-1426","524","-1918","-68","448","496","-768","924","914","400","-400","-1984","712","384","218","-80","-192","320","1426","-480","-408","256","2513","-1624","-44","-832","96","1104","1224","-128","624","1984","-558","-496","-480","432","1600","136","934","-48","-70","1536","-48","-1464","-3844","-368","1280","-356","-466","-1424","3230","524","-408","160","391","-2976","-3328","496","-1466","-1400","924","-512","-288","-842","-542","88","-1984","1984","2704","384","1647","544","460","-1248","1848","320","3144","992","-480","780","-3780","-1472","-3988","2976","-1624","96","-5696","-832","-1054","96","2400","640","1952","-128","-3402","292","1984","932","3284","2852","2220","-1048","432","3836","1920","136","352","-896","276","-992","-1240","1536","5582","-1848","-1464","-1828","-4992","-800","-4992","800","-356","3968","1054","-1424","6088","-768","-3013","-436","3274","160","-2930","384","-2976","-640","5858","-2852","384","960","-1400","816","-2640","-512","2102","-5026","-3542","3248","3728","88","1240","1664","1984","-192","1192","-2208","-744","-2448","544","256","-826","-1248","-8544","-3968","-1840","1116","3328","992","-7392","960","780","-864","1800","-3200","-3968","-272","2976","-1868","8122","96","504","140","4784","-3072","342","96","-2922","2928","640","7688","528","736","289","-2560","292","712","-1442","932","3840","2848","6200","-6460","744","-1048","-7488","816","3836","-320","12992","-782","804","5952","-896","6656","432","-992","-4562","2932","-8832","2800","-4236","-1848","4960","1024","-1828","576","340","1684","-8122","1084","800","-176","576","3968","-8528","-3968","8188","-5408","-3456","-768","4234","-3294","-436","-1088","-12896","-920","-2640","2496","384","-3696","-2606","-640","6530","-6288","-6200","-1984","-8442","960","11712","-1560","816","7560","2760","2944","-6459","7976","-5026","-5952","2848","3248","-8556","-192","-506","11392","-11088","1664","11658","2108","-192","-192","-4960","-4800","-7090","-1280","-2448","-3904","5648","256","23808","6804","7176","-584","3310","-3968","204","-1864","1116","-6568","11200","-5704","2644","-4440","960","2096","7102","-864","12896","-7672","6736","-3840","-22072","-272","-3130","-704","-1868","1792","5760","-552","-15872","1984","140","2480","5170","-3072","6562","-11164","-552","3696","-2227","2928","19488","3656","7688","9984","-1988","1600","-13022","9984","-2560","-1600","240","712","2980","-7936","-5359","-2108","8648","2848","-6240","-12176","-6460","1536","13070","6026","1364","872","816","-6548","-23808","-320","-16406","5860","-1700","-768","-9918","5952","14528","1280","6656","-11716","-8196","5704","-5184","-768","2932","-1920","-19344","2800","-2620","-1632","10626","5280","-10620","1024","22072","-4204","576","10052","-2336","7084","8684","-6496","1084","-7456","17892","-176","-1360","-2480","-22816","-3328","17568","-3968","-6890","384","-5408","-2384","-3732","4416","-30688","1488","-3294","4896","-11130","-1088","4272","-512","-2000","1652","7168","2496","1488","17088","-3696","7936","2462","3680","22208","-2232","-6288","-6656","3536","-1984","-12023","14784","-5520","-1920","-1364","-1560","14624","1728","7560","-3600","14446","6400","9092","7936","7976","544","-6400","-5952","-6","3736","-18676","-16244","-1600","-192","16800","-1008","11392","-280","14834","-9568","19344","6144","2108","-684","-15912","-192","3488","5844","10104","-5856","-13710","-1280","13882","-15376","-3904","-1056","-1572","-1472","-20626","-578","6804","5120","-23808","-584","-28644","-1424","22816","2884","-17876","-1864","4160","-7680","-6568","-5696","7618","-12400","-6528","12920","-4440","-1488","7240","2096","2562","14976","4968","-1632","40208","-7672","5784","640","-3840","-25984","-1488","1564","-8602","-1608","-704","-11904","-9006","1792","-28070","-13312","-1200","-864","-9360","1984","-14839","9124","2480","-5864","6052","17664","20472","-5600","-11164","8472","19584","3696","-14446","-9920","-16836","-2048","10382","3656","-7522","-1152","9984","-680","16904","-3368","14880","16244","9984","-2168","6168","-1600","-8928","352","-4094","-1152","-780","-7936","-9318","17056","-2108","7936","-7680","-16376","-960","10816","-12176","6912","50344","1536","-8602","-8468","13100","6588","-5756","872","-3504","2176","-6548","25792","26878","1840","14944","5280","5860","-4992","28644","-768","25022","7392","-34224","5212","-1120","1280","-374","-13060","-11716","12576","-25838","12400","7120","3968","-768","16884","-46032","-1920","-560","-23424","-16100","3120","2496","-1632","-61504","-15120","5280","-5520","-23060","-5888","10752","12918","-4204","-15952","10480","10052","-1136","11904","-4283","-5696","5304","-6496","31138","17112","-7456","384","-13392","1012","-30380","-22784","-2480","22176","-20512","-3328","51680","-23316","22816","-4216","21936","384","1892","384","-2384","9920","-6528","9600","-1786","14180","1488","2560","14502","4896","-9600","7808","6256","-11296","-14880","-512","4350","-47616","1652","-13608","-16042","-14352","-27248","1168","17088","-6620","-440","7936","45384","-408","8000","3728","-23456","-2232","22714","13136","-6656","-22400","5232","11408","-50344","-5288","14784","8880","-16606","-1920","-408","-4192","8970","-14204","11036","1728","-4608","-25792","-3600","15344","27470","-13472","-17258","7680","7936","44144","-8672","544","6240","6260","34224","1408","11252","3736","10388","-3584","-16244","-11520","-33506","1104","16430","31744","-1008","-3968","-3961","-280","43264","-4960","-20800","-10340","-3960","6144","-17989","-13124","-684","22328","26352","1104","60312","-7392","5844","4454","4272","-5856","-40472","-38976","7360","-7312","-3906","-15376","-48960","-19968","-1056","3976","21808","-3200","29568","26044","-578","-19968","43400","5120","13392","3200","3358","-480","2304","-1424","-3776","-5960","2884","15872","9842","10718","-5232","4216","-7680","-17296","35844","-5696","29376","12480","26102","24352","-480","12920","-60480","-3072","-1488","-26140","-16640","-12052","7854","-2728","14976","-1744","-63808","-1632","-30626","13096","44114","47616","-20008","640","-61504","32812","-25984","-11720","-13392","3400","-34800","1536","-1608","19836","-45384","-11904","-46636","-29056","-10304","-2560","29390","-13312","-4660","23432","-864","16392","-16864","-11408","-5866","10368","9124","1536","-23668","-5864","-264","3840","38400","38688","4634","-5600","-11036","5240","8472","3264","-1422","-21252","31232","-10560","-9920","21240","22416","-2048","13473","-44144","-21022","8408","-54432","-1152","35704","-20104","-680","4672","-21448","-14168","-1680","-17368","16244","12992","14954","-2168","-24180","14912","9200","-35784","16428","352","52544","2720","-1152","4960","3744","45632","49772","6656","17056","-35136","35520","7936","3844","13780","-35600","-768"]},{"label":"34.4.a.c","letter":"c","dim":2,"charpoly":["-116","-2","1"],"traces":["2","4","6","8","-4","12","-6","16","-10","-8","-6","24","-64","-12","-116","32","34","-20","-36","-16","-44","-12","42","48","174","-128","-36","-24","428","-232","86","64","372","68","116","-40","340","-72","-556","-32","404","-88","-620","-24","-604","84","-56","96","-642","348","102","-256","28","-72","-1548","-48","256","856","276","-464","-236","172","-126","128","1584","744","536","136","-108","232","1542","-80","-164","680","938","-144","-372","-1112","-1854","-64","-202","808","-372","-176","-68","-1240","1804","-48","-1976","-1208","556","168","-340","-112","-1384","192","-220","-1284","2370","696","1376","204","-1680","-512","712","56","1326","-144","12","-3096","1644","-96","-3028","512","852","1712","-1864","552","-102","-928","3206","-472","-1076","344","-1512","-252","556","256","-1392","3168","2294","1488","-256","1072","1528","272","-1080","-216","2806","464","3680","3084","-5268","-160","-2936","-328","-1770","1360","-420","1876","68","-288","-170","-744","2220","-2224","-196","-3708","-3868","-128","108","-404","674","1616","-5112","-744","-4178","-352","2750","-136","2364","-2480","-1684","3608","-938","-96","48","-3952","3156","-2416","1788","1112","540","336","-3176","-680","-102","-224","472","-2768","2168","384","-1684","-440","8808","-2568","6212","4740","-2450","1392","-1720","2752","-1804","408","8344","-3360","-1614","-1024","5568","1424","2026","112","3612","2652","-632","-288","340","24","3564","-6192","-1088","3288","-5180","-192","1626","-6056","-1286","1024","5352","1704","-2208","3424","2820","-3728","-15280","1104","-8396","-204","1216","-1856","-1684","6412","-5406","-944","660","-2152","-3944","688","-2832","-3024","2352","-504","-3636","1112","-1972","512","-6816","-2784","-1644","6336","980","4588","876","2976","15752","-512","-5668","2144","-9612","3056","-10208","544","3592","-2160","5718","-432","4932","5612","-4018","928","9732","7360","2938","6168","-3008","-10536","1076","-320","578","-5872","-2740","-656","12284","-3540","2568","2720","-5352","-840","1932","3752","1392","136","1060","-576","-4520","-340","8216","-1488","-5456","4440","3558","-4448","8964","-392","1604","-7416","476","-7736","6516","-256","-1092","216","-612","-808","-11392","1348","6172","3232","-3680","-10224","8308","-1488","2044","-8356","12240","-704","4628","5500","-4820","-272","-9228","4728","3828","-4960","840","-3368","-18790","7216","-628","-1876","6248","-192","-2188","96","972","-7904","-748","6312","7092","-4832","-7974","3576","7278","2224","-15896","1080","-8550","672","-15748","-6352","3868","-1360","17328","-204","-1416","-448","-20976","944","-15914","-5536","-2856","4336","1948","768","5112","-3368","5908","-880","-13352","17616","714","-5136","18556","12424","15044","9480","-6332","-4900","-1392","2784","-5268","-3440","5620","5504","23492","-3608","8340","816","6996","16688","2844","-6720","-48","-3228","7608","-2048","-708","11136","5514","2848","-2784","4052","23368","224","2958","7224","-540","5304","-27192","-1264","1682","-576","-10384","680","-32104","48","-4032","7128","8278","-12384","4146","-2176","-20184","6576","2912","-10360","4980","-384","-10508","3252","-35532","-12112","18872","-2572","-8808","2048","-1104","10704","-612","3408","7100","-4416","-3512","6848","3384","5640","-19212","-7456","1720","-30560","17924","2208","8880","-16792","2692","-408","-23852","2432","19294","-3712","-19616","-3368","480","12824","8760","-10812","-16134","-1888","11876","1320","19372","-4304","7276","-7888","4932","1376","-3612","-5664","11890","-6048","-17188","4704","-13934","-1008","9520","-7272","31546","2224","22988","-3944","-3564","1024","-4448","-13632","5024","-5568","57888","-3288","460","12672","6020","1960","-29232","9176","-6324","1752","1462","5952","-21346","31504","-6060","-1024","19104","-11336","17628","4288","24912","-19224","4266","6112","11948","-20416","4636","1088","-24568","7184","-5490","-4320","8668","11436","-424","-864","8396","9864","-28456","11224","-11632","-8036","13288","1856","6324","19464","10940","14720","-11000","5876","6378","12336","-3228","-6016","-33494","-21072","-22304","2152","-90","-640","-1000","1156","-17428","-11744","2832","-5480","-59364","-1312","16416","24568","-29484","-7080","-9920","5136","11356","5440","1524","-10704","1972","-1680","-4932","3864","16040","7504","5580","2784","-22648","272","2948","2120","30078","-1152","-12536","-9040","-52080","-680","-5764","16432","8600","-2976","22932","-10912","28458","8880","2520","7116","5668","-8896","-31206","17928","8592","-784","5780","3208","-35372","-14832","-7884","952","16984","-15472","18360","13032","-13794","-512","6196","-2184","-20538","432","29408","-1224","35008","-1616","-12528","-22784","1696","2696","-20380","12344","-51284","6464","25156","-7360","23520","-20448","-10548","16616","-9452","-2976","3008","4088","4308","-16712","-12264","24480","19428","-1408","55332","9256","-8956","11000","13676","-9640","2740","-544","5684","-18456","-6834","9456","-22176","7656","7060","-9920","54432","1680","22530","-6736","-4692","-37580","30892","14432","6868","-1256","33420","-3752","16752","12496","2616","-384","-50624","-4376","-1060","192","-6428","1944","-7734","-15808","7188","-1496","56088","12624","2192","14184","17814","-9664","5456","-15948","-13684","7152","45556","14556","-18312","4448","-20878","-31792","-10540","2160","-55492","-17100","35052","1344","-51528","-31496","57284","-12704","-16928","7736","-10714","-2720","-24120","34656","-8436","-408","1092","-2832","-8498","-896","-16344","-41952","-74808","1888","21352","-31828","-2016","-11072","43576","-5712","-6172","8672","-10268","3896","2088","1536","-27464","10224","-4692","-6736","-7608","11816","-2086","-1760","-11224","-26704","-39304","35232","-19836","1428","-14984","-10272","-73656","37112","42470","24848","-34968","30088","4820","18960","-9920","-12664","53704","-9800","-56420","-2784","-952","5568","11440","-10536","61332","-6880","-840","11240","-33204","11008","27916","46984","41990","-7216","-16272","16680","-40764","1632","17712","13992","8764","33376","40092","5688","-13486","-13440","49836","-96","25834","-6456","-12868","15216","33100","-4096","-10914","-1416","26972","22272","6824","11028","-9966","5696","53214","-5568","24828","8104","-98684","46736","-7278","448","-10764","5916","1524","14448","21244","-1080","13784","10608","-31996","-54384","33844","-2528","4840","3364","-8136","-1152","-18680","-20768","1734","1360","-36948","-64208","29440","96","-11380","-8064","1416","14256","75740","16556","31444","-24768","-11404","8292","-22424","-4352","-5088","-40368","-33882","13152","2856","5824","-85974","-20720","54880","9960","-68088","-768","5640","-21016","6444","6504","476","-71064","10832","-24224","-664","37744","62186","-5144","-25288","-17616","-61582","4096","-24624","-2208","-3784","21408","-18556","-1224","29808","6816","35672","14200","-35148","-8832","39564","-7024","5904","13696","11324","6768","13740","11280","16524","-38424","-26316","-14912","24948","3440","-3476","-61120","-41076","35848","29076","4416","-7184","17760","-26250","-33584","-51536","5384","-42980","-816","35944","-47704","110896","4864","101448","38588","-2844","-7424","-42130","-39232","-37050","-6736","52872","960","-30348","25648","4352","17520","2780","-21624","708","-32268","-79156","-3776","-9724","23752","9828","2640","36756","38744","-17402","-8608","16696","14552","-21856","-15776","-17232","9864","-7802","2752","41616","-7224","-4772","-11328","-5004","23780","-14856","-12096"]}],"seconds":0.101,"computed":"atlas","estimate":{"seconds":0.234,"low":0.143,"high":0.405,"bytes":1842817}}