{"label":"10.4.a","level":10,"weight":4,"dims":{"new":1,"cusp":3,"eisenstein":4,"modsym":10},"old":[[5,1,2]],"T":[[3,1],[7,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 5, 10]: [1, 2, 3, 7] (certified at ell = 2147483629)","T = [(3, 1), (7, 1)]; h of degree 1 = 1 x 1 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"10.4.a.a","letter":"a","dim":1,"charpoly":["12","1"],"traces":["1","2","-8","4","5","-16","-4","8","37","10","12","-32","-58","-8","-40","16","66","74","-100","20","32","24","132","-64","25","-116","-80","-16","-90","-80","152","32","-96","132","-20","148","-34","-200","464","40","-438","64","32","48","185","264","-204","-128","-327","50","-528","-232","222","-160","60","-32","800","-180","420","-160","902","304","-148","64","-290","-192","-1024","264","-1056","-40","432","296","362","-68","-200","-400","-48","928","-160","80","-359","-876","72","128","330","64","720","96","810","370","232","528","-1216","-408","-500","-256","1106","-654","444","100","-258","-1056","-988","-464","160","444","-24","-320","950","120","272","-64","-1038","1600","660","-360","-2146","840","-264","-320","-1187","1804","3504","608","125","-296","-124","128","-256","-580","132","-384","400","-2048","-400","528","-1254","-2112","-2860","-80","1632","864","-696","592","-450","724","2616","-136","750","-400","-448","-800","2442","-96","760","1856","2246","-320","-1776","160","-528","-718","-568","-1752","-480","144","-1524","256","1167","660","-3700","128","3702","1440","-100","192","-3360","1620","3180","740","-2098","464","-7216","1056","-170","-2432","792","-816","320","-1000","4392","-512","-2158","2212","2320","-1308","-1074","888","2840","200","8192","-516","360","-2112","-2190","-1976","4884","-928","-1200","320","-2668","888","-3456","-48","160","-640","-608","1900","-2896","240","-3828","544","1772","-128","925","-2076","-2784","3200","350","1320","384","-720","1962","-4292","-1020","1680","1280","-528","-4320","-640","-478","-2374","5032","3608","-1635","7008","5800","1216","-576","250","2652","-592","1584","-248","-2640","256","-2334","-512","136","-1160","-3330","264","-3948","-768","1110","800","-6480","-4096","1590","-800","4952","1056","-1856","-2508","300","-4224","1646","-5720","5624","-160","-1158","3264","6992","1728","4000","-1392","1752","1184","-557","-900","-8848","1448","-258","5232","2100","-272","-960","1500","-7656","-800","-128","-896","2064","-1600","4510","4884","-8944","-192","7904","1520","1392","3712","-5878","4492","-740","-640","10326","-3552","-1080","320","192","-1056","-6600","-1436","-1450","-1136","-7600","-3504","816","-960","-4228","288","-1258","-3048","-5120","512","1106","2334","8304","1320","1824","-7400","2680","256","-5280","7404","9336","2880","-11770","-200","4640","384","8322","-6720","2160","3240","2112","6360","10680","1480","3141","-4196","9496","928","1810","-14432","-5884","2112","-16206","-340","-888","-4864","-2098","1584","-1000","-1632","5220","640","3860","-2000","992","8784","-9588","-1024","-240","-4316","1184","4424","-13410","4640","8712","-2616","-1056","-2148","-800","1776","-13114","5680","-3200","400","-5838","16384","-8816","-1032","-1795","720","-408","-4224","9530","-4380","10032","-3952","-1680","9768","360","-1856","22880","-2400","7260","640","12062","-5336","-7548","1776","1650","-6912","-3608","-96","5568","320","-13608","-1280","-3838","-1216","3600","3800","-13200","-5792","7400","480","-12099","-7656","8352","1088","4050","3544","-6000","-256","10770","1850","-5256","-4152","3584","-5568","1160","6400","-6694","700","-5280","2640","-3018","768","14492","-1440","-6080","3924","7776","-8584","4096","-2040","-17968","3360","384","2560","-2500","-1056","8214","-8640","-13680","-1280","1972","-956","4224","-4748","5530","10064","7916","7216","4544","-3270","13932","14016","-5940","11600","2220","2432","-1728","-1152","-8260","500","12192","5304","-11148","-1184","-1290","3168","-9336","-496","-9690","-5280","-1448","512","8000","-4668","-4940","-1024","-2448","272","-29616","-2320","-16038","-6660","992","528","800","-7896","10032","-1536","5257","2220","15540","1600","25404","-12960","-120","-8192","-25440","3180","-3924","-1600","7142","9904","16784","2112","4750","-3712","7616","-5016","33374","600","9000","-8448","640","3292","1360","-11440","-10314","11248","-1856","-320","-6336","-2316","-7128","6528","-5190","13984","1436","3456","2010","8000","-23188","-2784","-35136","3504","3300","2368","22466","-1114","17264","-1800","-288","-17696","2664","2896","-10730","-516","22776","10464","-15200","4200","8592","-544","-21198","-1920","-1320","3000","-22720","-15312","15960","-1600","5882","-256","-37888","-1792","-5935","4128","8516","-3200","-2880","9020","11832","9768","8462","-17888","17520","-384","-11094","15808","2180","3040","-10560","2784","-3240","7424","625","-11756","9600","8984","-2244","-1480","-26848","-1280","21344","20652","-620","-7104","18966","-2160","15984","640","26322","384","-10168","-2112","-1280","-13200","-23604","-2872","5040","-2900","4864","-2272","16422","-15200","660","-7008","13394","1632","-26100","-1920","-3058","-8456","30624","576","2000","-2516","-11880","-6096","-14176","-10240","10824","1024","10802","2212","-2000","4668","-10674","16608","-4424","2640","22272","3648","-28608","-14800","-6270","5360","-2800","512","-12876","-10560","-2428","14808","-1776","18672","-14300","5760","-28908","-23540","-15696","-400","-6618","9280","3400","768","8160","16644","1032","-13440","20510","4320","-5920","6480","20064","4224","-3480","12720","34560","21360","31680","2960","3952","6282","3824","-8392","-2250","18992","13196","1856","-30563","3620","2112","-28864","8102","-11768","13080","4224","-12288","-32412","-12580","-680","-46400","-1776","29892","-9728","3750","-4196","2664","3168","96","-2000","-40408","-3264","-21216","10440","-2240","1280","32366","7720","-12672","-4000","-17238","1984","-3800","17568","12210","-19176","-24360","-2048","10850","-480","18672","-8632","9102","2368","3800","8848","-1088","-26820","43800","9280","5184","17424","7200","-5232","11230","-2112","-25504","-4296","31584","-1600","4152","3552","-52316","-26228","-8880","11360","14166","-6400","-13464","800","29970","-11676","4344","32768","-2640","-17632","-12720","-2064","33210","-3590","39212","1440","-39616","-816","-2840","-8448","-3200","19060","8584","-8760","6222","20064","31172","-7904","-2400","-3360","-264","19536","-29050","720","-13168","-3712","-21582","45760","-7620","-4800","-12160","14520","-21720","1280","-16289","24124","9264","-10672","5835","-15096","4748","3552","-55936","3300","-4488","-13824","-6658","-7216","-18500","-192","-13974","11136","23780","640","-14016","-27216","-12228","-2560","18510","-7676","4456","-2432","-1920","7200","59392","7600","40922","-26400","-500","-11584","11606","14800","2064","960","-32958","-24198","8072","-15312","-16800","16704","15756","2176","496","8100","-4308","7088","20400","-12000","15900","-512","61248","21540","-13680","3700","14652","-10512","1024","-8304","-10490","7168","18776","-11136","-9546","2320","-20568","12800","864","-13388","-36080","1400","-528","-10560","-6280","5280","71552","-6036","-25056","1536","-850","28984","-36556","-2880","-20430","-12160","32700","7848","-11136","15552","3960","-17168","8906","8192","47024","-4080","-17418","-35936","-57816","6720","1600","768","-2544","5120","-20996","-5000","-82608","-2112","15402","16428","21960","-17280","8640","-27360","5016","-2560","-6687","3944","-888","-1912","-10790","8448","-49444","-9496","52800","11060","-25188","20128","11440","15832","11600","14432","2946","9088","9720","-6540","35150","27864","15012","28032","-5370","-11880","-6528","23200","4224","4440","-5128","4864","33824","-3456","14200","-2304","-49714","-16520","2720","1000"],"derived":{"al":[[2,-1],[5,-1]],"fricke":1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.118,"computed":"atlas","estimate":{"seconds":0.223,"low":0.136,"high":0.385,"bytes":1811990},"url":"https://sagebrush.space/atlas/mf/10.4.a"}