{"label":"41.4.a","level":41,"weight":4,"dims":{"new":10,"cusp":10,"eisenstein":2,"modsym":22},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 41]: [1, 12] (certified at ell = 2147482921)","T = [(2, 1), (3, 1)]; h of degree 10 = 1 x 10 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"41.4.a.a","letter":"a","dim":3,"charpoly":["29","33","11","1"],"traces":["3","-3","-8","-5","-10","-18","-50","-15","-9","2","-38","68","30","124","6","11","42","177","-148","106","72","116","52","162","-203","78","-134","-238","-54","-34","-464","357","84","-410","-106","-245","-126","-26","-508","-130","123","412","-204","-370","350","-236","424","-264","559","287","688","158","438","90","-350","400","972","-598","-48","-34","74","480","220","-805","856","488","-874","538","-412","214","-1140","-1023","1038","198","792","136","1760","-1032","-2760","-834","1059","-123","136","-1148","-764","-1776","1456","632","-1446","86","-1768","1564","740","1142","-598","-1074","262","-4063","-380","-667","1010","676","-900","-1962","124","2110","1864","-430","714","330","-286","2142","-1914","1924","2208","1378","4074","2424","-988","350","-1709","4258","-328","1672","336","-4658","848","-87","3004","-296","660","-1208","3724","1020","-1080","2014","-462","-1868","-5396","-154","-3364","-890","-3136","551","-504","-3766","2722","1022","-4390","2306","-5132","2986","-6414","-5280","3424","3028","1682","2674","-3440","1818","-5724","-2775","88","-205","444","5440","-6086","-2600","2013","-212","-4918","7300","4458","1652","6482","3258","-3228","214","3738","-3230","78","548","-7624","-3188","2404","1356","300","-5636","4740","186","1894","-1836","5558","-5886","-1644","11667","4810","-4894","-282","3107","4812","2410","-348","-2440","-410","8632","4780","-3266","4856","592","6946","-11474","6768","-5608","4700","3114","4508","-4102","2170","1682","-8124","-822","-2600","-12564","-3155","-3870","5776","-6352","170","-1432","-522","3578","-14262","5370","-3442","-7464","7828","11336","2968","598","-5850","-1619","4744","-11262","5814","-738","-11492","-552","-12016","536","8956","11720","-8996","-1736","1940","3259","4458","684","-1102","-6064","-9714","-9280","13260","-3508","-10208","-3768","6060","-4382","-7934","608","-548","-1510","8532","-418","8014","4196","-11706","3596","7216","334","6550","-2980","11092","6624","1776","676","-2050","3633","-839","-672","11504","4762","-4486","-4732","-3048","-2598","6516","11290","16448","-6860","-11060","3942","-14092","2652","-864","2062","2592","9844","-9104","-1224","-1502","12936","-1650","-3414","1250","4180","-11962","748","788","4866","440","14356","9000","631","-13078","12672","8500","-615","2356","552","-10690","-10376","7194","15664","-8034","4736","-8550","12099","13998","7324","-172","-12512","-18742","1920","-3008","-13186","-14268","-6496","-522","-15348","-13252","-15468","5898","-276","3098","5394","-13760","-12608","-9000","1394","-1073","14510","9090","2632","-4116","-5396","-5664","-14108","-369","-968","17564","-7132","-2702","11832","1020","-4558","-12516","-8384","-7160","3106","-6508","-13760","1794","9330","2088","-11198","-11088","8902","15066","-980","-8776","-2047","19368","1890","7930","16736","-9946","13320","-14118","8301","3834","13272","9608","594","-7318","15936","-4618","-14564","23094","82","2864","-21884","15324","14980","7128","22350","13308","-3484","13668","-1940","-16074","-384","11434","2014","4518","9904","16092","8536","12276","-5116","-16636","6570","24670","-14508","2548","-1670","-20596","-2326","8698","-1326","-20693","-11068","200","1066","4628","328","-7064","16962","-13514","-19681","-1558","20106","8608","-6926","-836","-22520","-982","-27942","8428","-14096","21330","-12126","-16172","-5254","-3784","18270","-400","-31246","34272","3646","6628","-3264","-16916","17620","22652","-27652","3018","-14734","-9146","-2898","14376","534","5984","13751","-10316","-3798","-25112","-14606","-20936","-8722","-7280","2788","20300","-10792","7102","-10880","12616","-13472","20600","-9624","-1700","-20624","-19456","11458","18288","15868","-28704","12408","14126","388","-26382","-20595","20640","31574","-5108","-9964","6312","-1966","-6896","3472","-20346","-2026","14828","8364","-9300","2258","-18176","4124","5435","8488","19032","2432","1230","10360","-1648","20280","-11992","-21606","-43420","6128","-7866","4180","-26792","-3690","-20280","17180","16500","2786","49910","-15812","18592","16612","47900","11162","-3408","21956","9566","-19032","7320","1622","-18040","-7246","4914","15848","11292","-34252","-17456","13858","4082","2484","-5486","12160","18684","5084","-30812","32531","24130","6407","1380","5488","5376","12540","31164","5342","-15272","7042","18854","4206","6220","5136","-22216","-9446","33930","-8680","-3564","3458","-8340","-688","-6520","-21418","14010","63508","-28468","25848","10862","-26576","-57380","-38442","-25564","6856","5468","17002","3558","-13108","246","-8412","-55986","1816","-14844","-29600","-28144","30604","19816","-5196","10487","-6062","-19202","-14638","-15540","-7502","-4700","16006","-28016","23726","20376","10544","26378","17368","-23046","-13226","2366","-9928","-9386","-23692","-1488","26964","-37120","6393","18756","-5102","-2168","-35304","4890","13376","-26372","451","-37818","-36208","11636","-4388","-2990","-5208","52952","-31568","4644","1026","-10608","-11466","-5400","5110","15148","10404","36602","-1098","26646","-41355","-53462","15030","-8932","-3596","-9536","-12372","-13140","45238","1172","109434","52268","-46588","-34476","-1504","-86308","34954","-23656","10454","34912","-29260","1722","-16030","32832","26422","50442","-7116","-12242","9486","-24","-40650","-41904","8148","-37598","-3454","3438","11830","23824","-1864","12020","51038","-3684","-3816","19000","22518","58184","37369","39136","-34490","11846","10540","752","23204","-57165","-3072","24504","27672","27082","-27020","-1638","58404","47124","7257","-77712","-18628","77748","-84304","1628","-9060","41416","10238","89248","-38812","-53096","7220","-9734","32056","-1000","-22316","45746","11716","13506","31920","12048","1194","-35578","-21380","6720","20570","12244","15388","408","29432","28438","-8084","-57108","-7826","-90626","18924","9800","32538","8244","-16098","-6068","11572","10124","-35336","15820","-81889","-37936","24944","-21260","-29438","-61208","-1334","1614","11606","41596","19342","7628","-59574","31170","-35082","-22608","-58569","-11022","4982","-19882","-38056","-4224","-8760","51872","-49502","-21814","26","-22828","-39964","7612","-818","-6808","-912","5084","-5518","-29524","4346","-4190","4148","38704","-10400","-14296","-83868","19022","-73484","44854","4664","18970","28942","52866","21932","24958","-3820","-1000","-17192","37058","-3296","-38051","32838","-34280","-31962","-12150","5708","6964","78470","25260","45666","31328","-39756","-4062","-131848","3326","-3064","7522","20716","5920","-27428","2952","51104","16752","-47478","26268","-44046","-11928","32780","38808","1932","-89312","35138","-96602","4460","21764","5330","65434","-11184","43176","-12030","21950","90305","55352","66116","-1224","-82948","97526","11850","-58068","-2716","-6680","42632","-27048","-2372","57726","12848","-60920","13350","-6440","63041","-7628","4756","-51156","22446","3960","10800","352","-14460","102974","356","23256","16132","-8240","-16410","-9756","60906","-1024","32524","-9134","11672","632","14054","-37980","31814","-14326","14558","71160","-12966","-73942","4296","-41318","10122","-31864","-10144","-16964","-50886","-10618","-70720","15316","22918","-92222","16320","2132","46752","5212","71012","71440","-65320","-23184","1154","4820","-20992","-7714","-30086","-18190","57188","-32396","9668","5044","-9794","8803","1896","-36824","-5426","-43852","41032","72934","12445","-91784","-3540","-40448","18260","53564","33324","73524","59674","-17942","-11592","14936","-19974","-96498","13712","-24108","6642","-25376","-1428","51942","58652","70744","-11082","-53708","-15984","36304","13372","-53958","51200","-113634","-18018","-17800","15920"]},{"label":"41.4.a.b","letter":"b","dim":7,"charpoly":["-82714","125528","-49882","2408","1655","-199","-5","1"],"traces":["7","1","4","43","10","18","48","33","99","82","34","-218","-60","-304","46","59","-82","-563","144","-410","84","82","204","-86","169","-292","46","0","68","-444","696","625","124","182","-6","831","730","34","848","778","-287","-4","368","230","-1510","432","-26","-1770","679","-1137","424","-1308","-892","1340","358","-1976","-3788","1416","-916","220","-450","208","874","939","-1092","-576","-142","226","-3396","2208","390","-2875","882","1822","-292","4278","-2572","232","2890","38","951","-41","1368","3540","-1740","-132","-812","4506","-2006","5746","2284","4112","2508","104","-1002","-1782","-1950","-931","892","-2283","-2368","-2964","1200","-1092","-3836","-1716","2032","-2796","816","-4332","2430","-11104","-2622","8912","728","824","-2736","-280","4880","-6428","-3145","-3502","-164","1904","1632","-9384","1752","7745","2724","-10664","572","-4272","856","7818","9248","-7690","-738","7880","-888","-3072","-1168","-14156","1060","3599","-1148","-2210","4166","6810","1000","8062","1302","4042","-1466","-9388","6576","21208","1904","8032","8844","-1622","-1836","-12119","8960","-1763","1580","-8604","-5624","11620","7629","12348","-4970","-11724","-3266","13904","5876","12742","-668","-11662","-4110","-23082","5136","-1552","-11592","-1984","-3532","-12648","-14340","7832","540","-1980","3192","-11466","1410","3302","-22268","8031","7582","8866","11772","-10353","-4196","-3244","-19040","13284","-410","7560","3100","-27932","736","7648","4342","-12556","380","-6524","6804","29308","3188","-9564","-13018","-2356","-5504","-1908","7192","-10360","4673","11134","-21832","-20592","6612","18496","-1710","11320","890","21612","-18186","-14792","12784","15488","5686","27180","-38","13253","-24324","3862","1898","-738","4560","17120","-9136","-8092","15324","27848","-5212","26528","-8876","17179","7570","37080","-3526","6968","-1112","-18416","-16762","-19608","1548","-10732","3220","7310","2114","-18520","15828","-21790","7780","-16578","-2782","-45944","-10858","21784","7368","3264","5286","13596","-9216","-5828","-2104","-7416","-1968","12117","7077","-34640","1064","1754","11388","-49806","20888","-2602","11844","10900","-34240","-7190","4308","-2044","-8248","9734","-7208","-22738","80","-23988","3704","4832","404","-4824","5138","9172","-45422","14752","-8356","-30216","29184","20742","12016","6264","-14736","19907","972","-44284","5416","-1353","7976","6920","13858","4012","21322","23308","-4782","-492","16290","26875","-33534","10676","12580","-21086","13326","-52356","39368","-30238","-4968","-28400","18570","14112","5604","26490","-4990","-11288","-5698","-9066","27680","24398","14208","31450","26619","-8048","-6722","21872","14660","42100","24628","38256","-4059","29588","-6608","-13128","-2734","-21460","11792","-28032","20496","-24384","7780","-3748","-15212","-4532","-3716","-39190","-12696","-19570","6772","-13438","-15634","38640","7768","31205","8288","-25222","-8446","-25514","-24344","-6632","-25942","-26939","25526","22360","-16872","30172","-15298","-14624","-3298","27548","4966","-3362","-43752","18264","-15652","-55648","-1624","-49028","-17852","8504","13640","17760","13984","986","12552","-10212","-8998","20956","-3316","3116","-14356","-8872","7928","9508","-68470","-44600","17932","-3124","33836","48356","-12024","20308","739","840","-45648","-39724","-35276","-1192","39468","-36640","-14786","-15229","-1394","40698","-8020","8394","12004","4552","-5882","11464","-12284","-21280","-38062","32216","23706","47448","-776","-3838","-2828","-9436","-33140","24400","34960","1560","-15180","21428","5536","40800","25056","16468","-600","-2012","-40412","69990","-38608","-26441","44140","41158","32596","-27790","-9152","37682","14540","8938","-80336","3304","42526","29104","33900","49784","15416","24284","58616","11936","5410","608","-35212","4568","-964","28256","25144","8760","32522","37649","-46216","-2454","-20004","-9736","-29876","-21840","10048","12008","-12822","65864","-27676","-62544","-44664","-14920","-20784","-11984","-5841","24552","-10244","-64756","2460","3444","2208","-14014","44840","-61234","-15600","74296","-24774","-51960","-36500","-24362","-41700","-86448","8788","82682","18514","-40098","45380","35016","-29448","-72226","34296","39016","4456","-20288","8936","-51056","-4000","-414","11438","12596","-63852","41664","56162","-68228","-47650","-110024","17662","-22536","26496","12464","9412","-106177","48522","3091","12412","-18400","91320","-123524","-1128","-23114","9140","63456","-5306","59750","-31812","14256","47528","43770","-1918","-1384","-1236","-102820","-28488","-14272","20600","57542","-52510","117280","-18952","62540","48906","-96200","-15088","13482","-82980","24196","21912","33834","-25806","-111656","-1886","-28516","52694","-3832","35536","-19104","-60392","11764","22468","18776","-84781","-75290","-43870","49116","34548","90544","96116","-1624","92744","41212","59848","35400","-9088","66416","123424","-41014","42130","-6536","7530","-42504","71192","55564","50284","-103119","3804","30948","41368","43244","-73396","107432","60532","-2419","-33438","6068","38512","-52104","6190","-133050","53392","-98012","90236","-98402","-11744","-13964","7216","19524","-8016","140580","-27922","30746","-24922","51721","2006","126644","-23504","-82452","9328","14504","-13468","125462","-87588","2552","-24800","-111852","-45512","-156384","-5860","-47882","-636","106994","-43360","-67152","3362","88346","-21480","82992","-13974","-228496","-43050","56294","-23144","-17718","-44580","-42296","-67948","108296","56256","-37758","-2992","-125640","22404","-18502","48048","2264","-75614","58070","15528","-121187","17184","67712","-8036","-52366","-44010","193584","-4617","-6492","-5696","-95076","-66298","-24232","-108382","44992","-20724","23083","-34424","-57908","115492","24064","68640","-81224","117740","-36458","16800","-35196","-35480","17992","42184","-57368","-60456","105344","-46602","-94816","34916","-104824","15552","131396","20010","-50568","-1108","12180","-74276","124004","-99040","141270","-35234","-103824","-70252","-14982","-30464","16844","11376","151206","34508","18266","-5904","-87120","-11672","51232","-52676","-18993","-63532","72120","17100","21262","6532","-3968","-162674","-37574","-27144","98176","44812","76280","29642","237736","83396","-86977","47914","175254","-27554","-81384","38368","-150464","-148232","129652","57318","186554","-948","-137504","-20260","44476","-39240","-35068","-24180","89938","41496","16810","10698","300","109390","63160","42712","91016","-6478","116448","53474","89576","-171030","-53980","82958","65336","-62282","89800","124600","10972","92520","-69664","89053","-66352","12512","-65858","14910","-115888","-28130","25588","-2124","100682","53368","-102972","-72218","30416","-192094","17060","-15462","106400","49776","-78168","-3444","9416","-20980","141628","-56164","-99826","-5380","-26360","40084","-138368","-79636","-130076","-103766","-97352","41752","-43764","-12798","-15028","35460","81948","12474","-97551","51300","34104","115960","-5376","-35332","-212","-98268","-28508","-91556","81160","41404","12536","-21474","-69816","67624","-96462","-30616","68145","45696","-3362","-217836","-13114","79188","-91780","60528","-88658","40924","-84352","52612","-151568","-108800","74230","106280","11704","17048","-22744","58220","52992","82272","-72978","-77064","116952","-23510","-198432","-89540","-12360","45158","128256","-59694","78182","-24732","-146632","-167356","117788","13566","103692","22084","-34384","101822","-183656","-8364","92376","37188","-144104","-64100","-99300","24932","-154898","-52248","-19632","105966","33836","-29958","-34884","21172","-97128","59160","-141460","-53545","6856","165728","82162","-77828","263904","68652","20877","114280","-54100","85284","-155198","-90604","-5584","-64992","39798","61190","174472","2920","49430","147412","101800","55988","3526","-108056","-60400","51758","-284616","26296","17764","113094","160096","60616","-47636","69418","17896","27404","44494","-40296","-43740"]}],"seconds":0.093,"computed":"atlas","estimate":{"seconds":0.231,"low":0.141,"high":0.399,"bytes":1877905}}