{"label":"103.4.a","level":103,"weight":4,"dims":{"new":25,"cusp":25,"eisenstein":2,"modsym":52},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 103]: [1, 27] (certified at ell = 2147482501)","T = [(2, 1), (3, 1)]; h of degree 25 = 1 x 25 (phi(ord eps) x dim S_k^new); 4 primes, 0 rejected"],"newforms":[{"label":"103.4.a.a","letter":"a","dim":10,"charpoly":["406092","186260","-205527","-93071","33595","15022","-2024","-936","21","19","1"],"traces":["10","-11","-8","27","-30","-17","-33","-108","-24","-2","-28","-57","-75","-149","-206","-29","-401","-222","-171","-387","-236","-179","-463","-54","10","66","-218","419","-395","710","188","145","-142","1270","-342","912","-142","573","600","1891","-561","1303","-108","902","296","2298","-412","1275","459","88","252","767","-1050","1989","362","-670","-918","822","-503","-89","-629","-611","57","630","-2348","1055","-1054","-2145","-286","2144","168","82","-1642","-83","500","-404","-2376","-660","629","-3522","-1330","1260","-2013","-1849","-708","-141","-1286","-1991","-926","-266","-466","-7224","-2632","-592","-886","-275","-291","-2552","-492","565","-3680","-938","1030","-2905","88","2443","-1344","-4187","330","583","6044","5291","-4548","3629","6148","1304","-141","268","1663","3065","2496","-1657","3580","1511","276","4136","1172","-1301","-1576","2655","3513","1742","2198","1639","8800","5151","-10015","1192","8878","-4575","5838","-3372","-142","-2676","-1520","3706","8494","-2261","255","-974","5986","2713","-1361","-6249","6690","2417","2678","-7456","5700","6161","-6008","-1171","573","-9326","-3190","7531","-1752","-980","-1897","-2913","13749","-6179","-4440","2066","7543","6585","3898","-7748","-4189","892","8754","-4714","4590","6982","-4738","5203","-1974","1379","-5152","-10001","1940","1704","-2878","-12858","6416","3796","-6622","474","3862","-8455","-1930","1076","9363","-7019","820","-1133","-7121","-3220","-15766","-4648","3218","-16794","3178","-7041","1480","16126","-14320","-1203","11494","-13989","-1356","-22829","2213","-12731","-8230","2951","-490","-20980","-3705","-8982","13416","-13222","-22068","-8934","-4940","6553","12152","-4226","-10777","-9218","4144","-3797","3116","6338","-4914","4100","-125","9582","-10860","-2745","13024","-5492","-6810","19901","22662","-5981","-12044","23941","-3214","5820","5493","-8639","3188","-17429","2234","25059","-2356","-785","2029","-21364","756","5674","-8310","18015","16700","8792","-10712","-6220","26860","16395","4436","-15716","4318","10865","10860","31477","1166","12352","-7563","25334","9064","-12655","3508","-18194","15576","34956","-1422","-28997","9259","16963","17886","20023","-1108","-14437","-11654","21916","-906","30430","-824","-14884","20275","553","-15103","13241","5402","27911","2513","16449","-2418","3609","9446","12508","7060","-4005","-13645","23439","-15758","17510","-3898","28965","6300","-5070","-10866","-21479","6050","14587","-14329","15518","-8238","17238","-2766","-38492","-29874","4546","4622","30689","-2203","-17892","-5060","2592","-13180","-31484","-5932","-61132","-7804","53362","18654","22843","-27500","-23440","3463","-11755","-8584","-12407","-3330","-6967","-4013","-27092","-32937","-26556","-10478","-31875","-32371","12923","-13284","-3289","-17126","17919","-14788","44433","-26474","-5784","492","-13133","-19208","15697","6594","2420","-17598","-17687","8152","-6350","-41678","-21971","-1236","-22116","-24774","31260","-23650","32198","-35205","-5915","-14202","-15199","-4354","-39676","-24944","13433","-6657","-8662","7944","2781","-24587","-730","1872","25495","-49244","6056","4503","-10329","43864","38058","-25932","-3237","-16907","12","10591","4976","4020","10782","20387","-56839","13382","42503","30056","15522","-815","-54278","-15570","73384","-16533","-5765","5094","37381","-30836","302","1912","20184","-22486","45146","9534","-20057","17972","-23868","26818","51935","-18990","19643","632","71608","55026","-55531","15732","62482","18512","22629","-25333","10534","17076","27719","-14694","-3907","-56554","-92452","3993","2939","24254","42234","43128","-15637","204","28648","16132","-20682","46294","10830","6664","-4693","28096","25502","29593","18848","56745","-42375","15816","-49091","-15550","22117","23238","25821","28586","-37180","-5656","-27214","43350","47938","3710","-55370","10527","-30107","42418","25860","-20102","-46605","-3090","-63089","71824","78573","-13652","-5587","296","5096","-22831","21897","80860","-28337","-13442","42331","15347","-12169","-15105","-66544","34421","16664","-15840","12918","2080","36577","32242","20367","8919","-12677","37820","-55749","17768","47844","32193","-78833","24933","-123647","10866","40098","-13548","34283","6922","50769","-46540","-95386","10710","-67320","33716","-46827","74408","41881","46086","15936","43909","-20347","-48346","-51835","-39603","-32165","25498","-31960","-33293","-100050","-29010","-38542","-45150","-57038","23917","23678","-51818","14595","16382","-44893","-57182","69402","56640","44729","6082","-52739","-16036","1269","32034","60977","4140","5920","-31880","-100757","46970","-44077","-4956","-45809","65000","-12612","-52829","75534","20392","55901","-59138","-47414","-38571","-646","954","-50061","-40812","-1751","6575","30619","80672","-78743","-14304","-58852","37474","4270","-12350","22847","24956","-34482","-24769","-43425","-23638","-103365","-21818","-494","116320","-46836","29464","-8128","-26311","43929","-47935","-74586","31884","-2243","-61031","-14660","32300","55341","-91854","-62399","-52072","27979","33674","-6582","-31582","-27548","5903","-70535","30860","-64825","-86534","63863","17788","109970","-1426","-33827","56744","50690","-25914","-100511","44683","-43203","6868","-114885","-54699","55065","-67135","-107303","-11650","38893","-76474","116944","88584","59333","69530","11267","11062","-118606","32568","-66400","91474","-20467","-43340","59374","30178","117842","20298","28969","-21946","11084","4888","73005","-12318","-18108","53156","178915","138253","-31587","-26893","-157490","-5086","-93002","-57098","-22642","142724","66404","-56644","68194","-3399","-41653","-3986","77262","-45089","11261","19742","97125","30840","29231","33592","-41810","34008","-3887","4934","128204","-65774","74360","38645","46853","10244","177719","-25740","109870","57982","-61381","-53249","-34483","2318","-16075","-31191","134384","9548","-37720","-23186","-99317","56705","52523","33332","-144082","-4946","138339","-26904","-245","-10980","-126169","-70552","49195","78638","158109","-134950","77815","90072","-79640","-114228","-10632","-17776","44994","-94281","-20496","88516","-183520","-50056","-49952","-107690","85749","50203","72073","40746","158831","-27744","93014","-31694","147860","-72940","65140","52955","146703","86850","-78815","79706","70304","-167666","-14303","88742","-33286","92848","127859","-141134","39682","-2584","140868","-8108","68055","-67904","7686","45200","21403","17480","89094","-79857","-38707","-144468","-11124","-50508","109266","26740","-31264","75332","-128303","17528","-7071","-69345","98200","-50458","-86329","496","54454","-9301","101389","-23831","16185","-15222","-189049","153212","168004","-771","13967","-64586","8391","-105234","45927","18786","-15969","-36242","46437","-135105","-69553","-101012","102807","57780","108966","-54602","3823","-39652","-157447","28272","-76947","-35436","-47614","41714","53163","41123","-163698","-138754","179143","16830","-81727","-110378","-181609","-101494","-56182","-175943","-17322","-46450","-195282","-7068","-123492","27796","165894","17896","-8542","-133680","-20677","2484","-60109","21730","121629","5482","-151018","-49084","110848","-77868","220468","-152822","-176219","12779","-43888","-694","-55607","-4442","-100459","82798","-5963","88414","-20219","83392","-52680","-64120","-296232","-208158","-124187","-13774","106050","40784","-131090","-2472","-132688","23207","-4124","-153056","-60923","-112456","203155","-65162","27206","10282","-110829","-86806","-152284","20358","40971","82989","16532","51714","140995","-104536","277691","-210","244783","38162","49375","-156473","-170004","32808","-235051","162880","155108","157484","-126733","-71410","-42018","81268","-46385","-9970","-74952","48990","22837","-20908","65732","-90844","27574","132226","-160481","103760","128383","-203949","-126687","212652","-7024","-57266","-69876","-52581","-66556","-151408","-125364","125262","14053","66336","-62174","-62232","126325","124284","157104","-2068","-32638","210546","-94449","43976","99368"]},{"label":"103.4.a.b","letter":"b","dim":15,"charpoly":["70653529840","129132221816","-50676583433","-43342961141","15632995657","2697205904","-1189103692","-56891893","39825892","-11640","-674833","17192","5688","-235","-19","1"],"traces":["15","9","10","67","30","19","23","132","201","58","126","159","133","19","-26","291","415","318","-19","213","100","217","365","378","885","201","-26","-784","173","-1954","-140","-100","-222","-1218","378","-236","-590","-486","-640","-1925","499","-2965","462","-200","-636","-1811","-28","321","446","892","120","-1233","1854","-3281","-458","-1709","1530","-306","-143","-4465","-173","893","977","-2426","2948","-2097","-732","2108","-330","-564","1708","2718","1048","891","678","124","3568","-952","1441","-634","4851","-447","2315","-3087","1828","2485","2026","1621","3320","16","270","2052","3000","512","4382","2623","2525","3883","3450","7085","2340","2510","-1545","359","2468","1875","848","-2907","46","1543","-9412","-2645","7266","831","-1304","4667","3427","-88","-3449","-11623","-6379","255","-3916","227","-396","-8516","-1188","119","-3384","-1193","-2903","-3138","-5602","10105","-21452","-7890","7633","-8566","-12802","7783","-2306","-5460","-1522","276","-7364","-1978","-2132","-8829","5599","3410","-7622","4789","-3029","-1697","-1870","-14489","-886","85","-2240","-14059","4640","15333","-6583","1986","-12234","907","-6868","-12198","592","7801","-21331","16825","8012","15052","-22357","6803","6702","-4844","3399","-2334","934","16717","-7662","-2210","13210","7571","-7866","8307","-1640","-3483","-6652","13024","5724","10322","-23088","8468","15598","13894","4214","24273","-10454","6952","-457","8993","5156","-927","5195","10269","5318","15816","-15940","25486","7218","15895","828","8304","8728","20375","-8190","2187","3172","1415","-16711","-931","27897","5717","11564","26606","1535","10110","-19356","5647","25070","27285","-12500","-7234","16944","-2557","-3369","-18958","3942","8183","-16802","3505","-8302","-19190","-19389","-13626","10560","4301","-12342","-7567","94","19491","-2154","-17629","14678","-9211","-5106","-13692","-1459","-1000","11680","8351","-13846","-42214","-13920","-14681","-3315","-46528","-17692","-11018","3618","13250","-1570","-31692","19248","-53188","10576","9547","-3658","18024","-12708","-7653","25900","-13847","6542","-23125","18314","-81904","-13736","15763","2800","25970","-4728","-42062","10938","3014","4199","11325","-11186","-20019","-17484","-2848","32318","-9084","3980","-24668","-1030","-34876","-8305","20037","-4855","-33693","21174","-801","15369","41177","10518","-55261","22194","25641","-7284","34471","-3765","-26297","11134","2214","16142","-23089","-9062","13631","-2846","38493","-19610","-55113","22831","-49102","4638","41596","-254","-48819","-17498","-1672","31994","-31441","23861","50790","10328","-67692","-33436","19808","31146","19724","12172","-73804","46954","23743","-13608","-55460","41998","6347","-9086","16496","17046","-85","3859","-19885","19723","24260","-41214","42673","-1883","-31003","5652","5201","30946","-11035","-2942","-7197","-5466","66126","15416","40897","10552","-54761","66900","32369","39010","8577","-7492","29494","37206","40373","-16712","25768","21278","-9122","21266","36786","-19785","45333","25118","9481","28866","-7097","9716","34885","35363","17406","20908","-6901","-17481","10057","41736","-81209","40368","13672","7079","69351","-10934","11200","-28588","88205","36669","-55368","19995","-33120","-21836","5510","13643","50595","25940","-45911","-26496","31710","-48369","-17078","-33134","-45712","-46162","28034","40352","-28131","-68060","-69395","-35460","-10020","-15064","118162","-15678","44409","-31156","-16404","-32142","-48355","-8888","-55313","37248","100082","9408","-41967","3044","73134","-63548","-32705","-8249","-7818","-51904","-125973","-1162","-2614","25350","11924","-30351","-113917","-73926","15902","10056","34635","21620","25422","27188","-74030","646","-111980","30288","-37024","-79712","17612","11469","41520","-73013","-29175","-10880","-5211","55902","24723","-31084","-112167","-2934","40420","40072","-57449","-6934","-38316","-3164","-4226","-4569","-33139","-11946","-33440","14478","56781","-3090","-46261","-40848","17037","-52192","6723","-38658","126732","29981","-11771","-95264","-12709","31722","11879","-43770","-30909","-22577","18583","-39297","78824","-55236","75936","-12828","22768","17988","-147241","-31217","-3113","48360","-24357","46388","60642","6409","33667","-170387","77919","-4182","-32046","41416","-79825","42714","-123539","20144","103976","2626","-24298","-7188","32695","62682","188093","-169586","-82566","76325","-1449","46932","46701","31249","18525","-140134","-31523","10039","-42650","-27908","13497","-1946","-121246","-23753","64424","-14494","-40543","74978","33155","-37638","122914","-78472","79351","-43778","25521","119742","-8739","48938","7497","-43188","16004","10180","167093","18116","28689","-4458","119027","-17976","124692","17555","94566","-110100","52365","-3318","-17029","43021","138442","66470","-1117","32258","-1957","-85433","22871","-31104","3229","66820","18578","96811","-35051","92082","65651","-90308","204876","22179","29707","91018","105159","38414","118650","-81338","-22056","102316","31980","95849","156089","-3571","64199","-247728","18212","-4311","114528","43540","46102","-89550","-56854","1016","60311","26298","27325","-20120","26350","7271","-120147","-4784","-3189","-11578","-50260","8300","41718","70758","-70415","-159300","134094","-10466","-82261","-78345","-42084","-104820","-39344","-26059","11441","-30207","-66501","37474","-126831","3096","21124","-21872","-93900","-15034","45297","-8962","34394","88930","-62534","1834","12860","18312","130082","19546","35500","18190","-316352","-16768","-166018","-21968","74535","34606","-17984","71764","-60161","-118211","-85671","109951","-25878","36398","-98382","-18570","-35873","-136836","-3472","-7972","-308848","-2369","-70353","88890","55674","-31345","2455","-88410","105876","76713","144883","49788","-87286","-59796","-16270","-9566","-98404","44410","-202935","43593","270157","-186140","-55053","64072","154306","28742","-62681","32015","-177579","-64354","-319211","47841","47920","98732","-109247","-3402","-160149","84929","-10395","-60020","60308","109264","-87077","-141428","-88529","-122240","-67239","80688","-130863","105748","138293","-87458","-275139","62534","182932","-42504","-9385","-86632","-25918","28491","-240396","-39652","-145063","-25832","102269","-85446","-84159","65091","228583","-103334","-212457","103120","38656","-8006","120990","99936","165656","15307","-69425","-37330","62314","30368","-87648","-88814","-34855","-120374","-12186","160260","-141779","91564","361846","126774","-23760","-132228","2903","30516","39790","-91504","-44925","-73608","278648","-2753","-16595","17428","-13596","-66680","-66715","28930","-167280","-121280","-120543","189260","-20442","171703","29386","-24730","58767","-96264","-95653","41335","129857","18898","94669","73398","-99999","215876","-30370","162997","242659","-23666","14583","22038","-172773","-208328","157674","47054","126377","104715","-164405","10398","46355","105292","-38854","68062","206719","143584","59743","-43234","-180891","-91992","-130954","23430","227415","86819","-91274","116182","74863","-11090","-161957","56418","-140197","43484","-180107","-21799","-15573","-293898","32448","172404","-212312","-99684","148410","305430","-141942","91252","155967","118588","33170","105034","-189161","170982","381530","55628","-12070","45896","209350","129502","-202079","-57489","29290","-144858","358979","112914","-58103","148450","242455","296606","-222834","113704","-278602","125012","25300","79538","-124987","209374","-98750","-204460","-33766","-20703","38208","119163","-44054","90468","231181","-172824","49648","91426","218342","32596","-32603","-27970","-129000","-25372","225815","25573","-73528","85862","219239","-142526","227413","-29566","101170","254070","-248777","162275","-150516","82672","-102518","-11904","42032","-108760","-141129","-68421","-330350","38084","419699","-65658","61064","62030","-111591","-139240","-83186","-35102","-522654","-50462","-29655","131772","101927","-80837","-156967","-17120","-76036","-247034","89736","-83165","-159004","50856","-156739","-930","-445968","-110944","154678","-38128","-148217","189548","308654","-233012","94170","-24802","24669","-218620","85314"]}],"seconds":0.102,"computed":"atlas","estimate":{"seconds":0.276,"low":0.169,"high":0.478,"bytes":2000173}}