{"label":"83.4.a","level":83,"weight":4,"dims":{"new":20,"cusp":20,"eisenstein":2,"modsym":42},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 83]: [1, 22] (certified at ell = 2147483323)","T = [(2, 1), (3, 1)]; h of degree 20 = 1 x 20 (phi(ord eps) x dim S_k^new); 3 primes, 0 rejected"],"newforms":[{"label":"83.4.a.a","letter":"a","dim":7,"charpoly":["8964","9644","1778","-1175","-406","18","16","1"],"traces":["7","-5","-11","13","-17","-27","-46","-57","16","-65","-59","-89","-205","30","-136","-163","-148","-188","-29","3","-197","-127","159","465","-108","603","217","24","29","1000","-420","459","-47","688","300","1000","-1091","327","286","119","127","1115","-49","795","-347","11","150","119","-521","448","-95","-1129","-785","717","-66","290","-434","-143","-81","-952","-195","1096","-913","-1203","-534","1517","-1825","-578","-1910","-2012","-666","-1284","-1594","713","819","-581","-1307","-610","-968","2347","-1193","-3961","581","-1655","-2407","-1197","3079","-1315","1616","313","1077","1127","-827","534","2252","2221","50","1071","3184","-1150","2734","-755","1056","1323","4144","2075","1415","67","-3365","806","5175","1240","-2066","-518","959","515","-2923","1363","6077","200","192","-2563","3958","-3694","-132","4119","-2184","2575","4898","998","4878","-4545","-5621","-1165","-742","564","-2244","3730","119","1676","4472","-1690","2944","-3112","-4462","-2510","5510","-8133","-555","-2353","1650","-3017","-2443","-4591","5397","3846","-7389","4608","7298","-1017","3944","-4481","903","3591","-4458","-415","-415","-2137","-3308","-6711","5377","-2681","-5171","-16721","2003","-373","-11921","-4176","-4733","1581","1726","-6039","4959","-5565","1880","5517","-6837","-5366","-2543","5488","525","-9","-7207","-7126","10378","1175","-5169","-7948","1147","588","3444","-2978","-7715","-49","-2544","13432","5079","2567","3368","-6508","5776","-11733","6754","4995","2965","-447","3305","2531","-8512","13326","8190","4287","-88","-6794","1311","15510","4674","2218","-2946","-11933","7117","9829","-2010","17025","-1552","11713","-682","8305","-348","-4968","12028","10164","3598","6751","-9126","16546","-4143","5596","-913","8516","4305","-8961","-11100","-8492","21242","15437","-7910","-9622","5103","2942","-1618","12014","14240","7433","-2030","-2549","704","2011","-4515","1066","13274","-1226","15568","-1812","-9439","-14438","-17404","8483","-21051","3012","-9582","-27580","-1326","-17446","-11138","12056","-1101","5220","3841","20918","-3284","12702","-16406","-29662","-2046","19309","-12065","8425","-14848","6269","-20454","-28646","-17374","13675","-878","15517","-9807","-4737","-16168","-391","4254","-19578","-7960","-9149","11070","-888","-8045","-20262","6431","-8797","-4666","12192","-26040","-13319","550","19475","-6931","-1577","-1834","-766","1097","1079","-28310","9493","-5625","10961","-4514","-25048","-8819","-275","10831","-22275","-5909","5883","3384","31405","13223","36489","-34827","21127","-7514","5705","-4630","24843","24806","20856","-11771","25143","-6638","-13951","7790","-16054","-22536","5229","19350","-24285","7900","10015","17425","21468","-1631","2227","-16861","-23773","22422","20822","9854","6221","15393","-13424","-8701","-24079","17802","-49319","16776","6769","13931","37362","13377","-49482","16767","6927","12684","-3669","-4338","7776","-26526","-6585","15380","10202","12327","37628","32778","14554","20335","3141","7551","-14439","30932","6016","-5638","6728","38031","-26005","-1411","-22781","27900","5204","-18177","15148","-9518","-7904","-16134","22259","26268","850","-8787","-3061","5590","42489","32694","-25837","-3258","-60543","-574","-29727","13262","65200","37084","-19258","24421","-40710","-15977","31321","-13166","-36024","-10758","6760","27220","-8873","12328","-46720","21657","-22210","-13859","13714","-23136","7338","-3767","-4777","-21481","30293","-38236","-58133","26662","24586","-2327","-54835","24444","27268","15584","-18105","-4532","-47494","2052","15655","-19103","-13908","-6038","-46896","52940","-41184","-18694","-29640","2764","10134","-9570","10225","-926","46354","-13913","-28074","-20967","6657","36888","9474","17780","-2241","-33179","-14884","-26733","-38715","-5344","-11449","2354","-56956","6041","182","20413","-6710","10040","-8253","19162","24262","-36584","42202","-60100","-28001","2311","18342","61777","37474","-27295","-10306","-32673","-68336","-17872","-2689","-18086","38226","-5460","-15889","-29707","-18024","-34196","-2053","16276","2273","31032","-42334","-10859","-9806","-45122","-33648","64150","-49340","-38477","-8488","48726","-27999","-27262","35442","36230","75416","14854","-20913","46142","86221","-25498","-11108","60933","-61546","-52333","78872","32474","5866","22250","55534","27682","4114","-8009","-58808","27387","56083","29809","-18072","-10642","85213","-584","-32506","-3818","-25452","-47916","-27150","25446","12382","29769","61678","-17692","-84702","-42047","47443","96614","5519","-49459","14469","63444","20000","25860","-15213","-22038","42586","15749","38484","58089","46250","25100","-18161","-10725","42358","-15590","-46307","-64179","2773","-77030","25101","43858","-52664","14975","24693","15208","22518","-75466","50766","-53507","-12128","-32110","26367","13071","-55610","-61518","36920","41020","-10881","54904","84254","22039","80435","-83592","14823","63602","-2682","-12065","13928","-70420","-59232","21778","50139","35027","-24462","115757","7447","-62431","82217","-96068","55215","41582","50290","-19704","-56478","-23568","-3907","9848","-4731","12689","91310","-91228","9603","-22568","-15253","-42097","-56869","18753","-7242","2691","37986","38377","43053","-17570","48465","-50640","87219","-83","48217","12260","22847","50250","38127","18811","76176","-92823","-86585","-9308","-56453","-99657","-32765","4500","-24187","7570","-1103","-40482","-12562","-45880","9195","15240","-53238","27168","-103263","-83177","40702","-31022","-41368","-82113","-138471","15042","-121589","6796","1086","76800","48997","-7864","-14750","-55223","42242","-39989","19004","-22128","19577","-51545","-31286","-77747","63949","-40103","-932","-16946","-23797","50530","-126499","23366","20564","-1406","53837","-48014","-54119","11411","12039","1328","-76139","28479","-104962","-71725","-36222","26234","-10222","-2041","-20609","-129903","73245","34008","-36592","484","134891","78315","375","22043","-92738","40732","55031","82688","33956","20854","20577","40550","-83457","-66244","7154","56031","-147799","-22297","94342","-107630","108035","36745","-61537","1063","-178764","23268","66665","-73906","-4518","-28966","-26452","-70754","171170","13758","-35093","-53956","92900","11132","-19792","99308","70103","119628","-60840","-53429","-91534","134730","-52202","81404","34399","14826","-58749","-59572","102547","-71692","72191","129932","96140","52119","64264","-101357","160978","11002","-53648","65759","-91013","94533","86567","19579","-5395","-44782","90791","-40114","-89224","7606","97900","-27491","9683","-29966","1860","36602","134602","46108","22716","70366","62274","40283","45595","-23194","67644","-116802","104326","69599","149177","-31744","-17973","-21844","-103198","140101","-74299","-137224","69230","75528","-27371","66178","-1306","-103838","44547","-94182","-18438","52034","49535","82766","-119402","-52637","-136404","-47623","-107788","74622","-96530","96762","-24831","-16950","42290","124474","72723","-33986","-164573","75570","49874","-45935","30652","766","-110542","46271","8474","104630","52008","60513","5543","35010","-91028","-62506","-23582","85938","66565","74315","34470","14416","100093","-8024","-38798","-4897","-241072","-54414","-67314","-62326","16345","118918","-5477","-62494","-31205","-4586","15027","-12035","71508","13896","44625","33956","-233438","69121","-77614","-124188","-44355","128176","73353","146126","32940","57681","-150452","-143189","28952","42622","-93039","-20906","33532","-121492","111506","27336","-123132","-30767","-72163","40349","49373","-3602","-54508","-8155","-163790","25476","131448","28899","-151200","-57847","79186","-82825","-76086","43454","-9940","116872","34516","-41877","43870","14740","-63610","-24016","-31497","-60448","-212954","165296","-65982","-134786","-4541","27299","14650","56068","-76471","-74424","32813","9589","-44272","27682","-44992","26902","-27652","-68486","-7387","-97741","48785","-96387","12740"]},{"label":"83.4.a.b","letter":"b","dim":13,"charpoly":["-3474959174","-1837881750","2605953954","-49861687","-308390534","21941285","14512388","-1210811","-320612","27544","3262","-278","-12","1"],"traces":["13","5","7","73","33","-3","52","63","178","35","7","127","237","114","104","365","-12","262","237","403","121","-121","-59","-1253","710","-505","-311","100","-255","-2548","-154","-971","-41","-946","-240","928","1169","-865","-234","-745","-351","-1649","1013","-2157","611","429","514","-945","721","-1668","-131","547","1505","-2131","414","-1078","1014","1639","501","-878","1649","364","833","2073","306","1111","2277","-658","10","484","798","2620","2042","741","2685","2107","2011","2594","808","5295","3117","-443","-1079","-391","3011","-1441","-1627","1447","1692","-2531","-2669","-2857","3831","2030","-3612","-9423","4274","-1847","-8456","7950","-5758","931","-2016","-1713","-3844","1063","377","-7373","2807","-2458","-8961","5388","-2450","646","-7227","-6293","323","5233","-8697","-18272","2642","1007","-266","1442","-48","3093","714","-3185","-598","2918","-7148","-5","3353","123","-14422","-5746","1464","9510","585","5606","-1660","7682","-9128","12248","814","-6434","-8242","11771","6915","-10117","5676","1471","-10109","6045","-12737","6024","9233","8588","5398","4451","-3576","21037","5105","3023","3402","-415","-6205","-6277","6558","10521","-10441","18253","-11","7405","6217","-8053","1513","7684","-2223","28591","10054","9857","-13547","18853","3124","19059","1987","9168","10311","4904","-11953","-1941","727","5322","-3834","-21877","5679","-6252","-6943","-17162","-5508","7850","-7163","5519","9968","-5936","-4071","-15113","6368","-23364","-14520","25401","18182","-9177","-14915","-40421","7943","-20397","-1236","-32824","5454","-16049","1796","-6848","24277","-22946","-5198","-1196","24","8919","-22111","11693","2746","6585","-19524","-8607","15490","-22807","7112","5794","308","4294","-8860","-4725","-3966","-1210","11873","-19256","-581","-55388","-8621","23111","16268","25342","13574","-30163","1362","4302","-1517","-7514","2832","-8754","5552","44101","13930","-17477","10692","-9275","10383","-57946","642","13446","23364","-35356","-3989","-34654","10622","23919","-3479","-32280","-8946","21908","-9666","22702","5090","-41816","6759","472","22455","25998","-10192","-20844","17344","20728","-878","37865","15097","-33603","-10584","54973","-11842","20872","1674","4795","13914","-37761","13091","-1277","9056","-30123","522","10602","6024","23791","28878","-20822","42119","-14390","17115","46015","6234","17110","-2344","81077","18038","3743","23753","-34699","32766","78466","8863","-6059","26954","-7547","-1","-22547","9214","34348","-15293","-47119","-6765","32377","-10357","15267","-22864","-44607","9589","-16071","9405","2073","-9506","18797","-24294","19719","4018","52996","1733","6747","-23972","-24007","-25108","-11166","-18718","-21715","-16510","-26871","4476","-36885","-84113","3564","-2581","59215","46647","-1255","16558","-48734","-39578","-30657","18231","-13612","-46453","-51433","20912","-23265","-58704","14059","38713","40306","-7897","-46810","-12009","37069","-1676","-24357","-26494","-107536","5572","-47","-27368","44478","649","14552","12934","-53598","17285","-61541","18909","91943","-15436","-14988","-3798","26468","-17013","50563","-2739","-53213","-65592","-57480","2145","-20214","39370","22488","4358","-27685","-87876","36518","19089","55497","3266","-24065","3768","-72933","23370","-1215","-12398","-231","21798","77864","14808","15474","-43523","-44826","3865","-22963","-12430","-12048","-2846","20864","-84120","67143","12488","-3616","-3779","8922","19973","39846","-39828","42094","-39587","-100583","10653","98861","22530","-3169","-99170","-7742","-48441","10899","14884","66952","50440","49045","-73508","57846","43352","-61645","54419","53088","-38084","-108264","-11004","70370","11832","25084","78712","-11740","39542","58985","-103814","63710","34129","132582","45223","-1497","-17668","-8474","-30296","249","25739","108560","-55129","18961","8436","48397","5530","-9654","6615","66","2317","207322","33228","11281","30654","91538","-124","107710","-244","66749","12271","62794","-33321","85526","-10193","34918","-26711","-81540","50224","-22925","-75562","-103802","77362","-39797","27307","37048","-27188","16799","-98280","-5783","130","-146696","38331","-108386","-44302","-980","-14202","-55932","925","-51764","16416","-47085","13498","92886","33342","77916","11238","-93053","-45490","-6025","2054","58686","-18685","-21206","-56091","-23062","79614","-61910","14918","34834","-4410","-22746","-2147","-126614","39461","-52773","-35181","80196","-38450","43015","-45716","-27160","-4316","-147456","45712","-118578","-157714","-70118","17995","-10370","-10316","72942","-7659","86451","-38090","81015","8783","62031","80816","-103452","37072","-273239","3878","-97226","88727","212308","63131","-21986","13766","-75017","-162435","85550","-1598","-310247","26335","65325","83910","54165","14642","-148096","3245","-224143","15910","47818","-61806","9608","-829","-25018","-50590","91047","-103467","-101270","30618","43092","-70104","-27429","108756","85170","149249","-140893","-7336","-61405","26138","-100898","35681","-448","29312","-36872","8202","144451","-68667","59606","82629","-3181","14623","53599","-80828","18583","-113906","27650","77072","5888","115712","-12799","-43692","-5229","-168183","102130","6448","-171981","-15280","23469","70907","-111235","57049","-50742","79651","57366","5887","-168965","76294","140505","-87096","69543","-22361","-40233","52448","55241","119142","150869","-43981","108356","-3625","-124337","14842","58539","-41393","32953","96380","-32915","97946","104921","-67052","71058","9984","-1517","-62944","-69604","50348","-155127","55073","-203058","72614","-28252","-673","-58891","144790","-10953","-33456","54478","56780","492151","51256","-163870","15789","113636","-15769","16986","114174","-226091","-126293","128846","105999","-138011","119517","264692","132858","71837","-38582","-351451","91692","185210","120794","4293","50070","286001","28507","24367","-14774","5941","63489","-267258","-21909","5792","-83902","66194","6985","-48061","43393","188001","102110","109788","-56808","-142073","67973","-179949","103837","-126786","39000","-16565","44364","231392","156562","66229","-52502","-160429","-102550","67282","-76495","-209687","-4627","-5282","-16218","-85177","-6469","-238977","22159","74636","-21846","70673","-89794","63794","634","-236388","-32246","19814","-134414","-105489","-32460","83012","-155228","-206180","98588","68805","190952","117364","-131571","13438","105974","2514","-124176","155295","-139946","-125989","78668","2701","-5692","73063","588","-168694","-49375","44580","-24723","17194","7062","136012","-120063","53321","-83781","-121773","-17479","-2905","-77506","26743","-115724","-84440","-55142","-67882","152595","-52447","-41784","-242128","13128","154274","169756","-142130","-16942","331318","-241009","207465","-151342","-79798","22618","224982","126455","144211","-51736","70215","-89996","-261142","-140109","104613","-76242","-121196","42298","-259263","44350","132506","-75398","-18429","-20990","258406","-28822","-394933","67594","-73322","-106739","61102","142119","-172756","-129894","-375368","102138","-272799","-27782","138248","-1866","222807","-56954","-442427","480","139998","-64103","81254","83638","-201230","-324985","187818","-12010","50844","-93743","594727","30830","80478","171834","-275288","119202","-38883","-14811","-51586","-172356","23755","87638","-27024","-581","101856","2978","-175790","-68630","-5551","-86598","255547","-53210","-86365","-12490","135403","225337","60984","-195028","128043","-4988","47506","38063","-72724","104968","-77219","81132","271565","-26230","-66088","-20575","-131928","-5233","129356","-167320","-168723","-162522","140916","-148668","65060","-34932","-41612","149725","-94249","-58427","347389","-265462","123520","-95295","-65714","-94560","334558","13437","-205544","-9917","164398","117493","105556","84710","315460","144356","-49408","-78519","-254930","204284","-5098","124268","74563","-53448","-4418","-184212","52058","119052","25527","164739","280310","-4232","236997","-209240","197225","-47325","149340","60428","-133530","95382","49188","186766","-10541","-124345","-37475","-158659","-318876"]}],"seconds":0.1,"computed":"atlas","estimate":{"seconds":0.258,"low":0.157,"high":0.446,"bytes":1958639}}