{"label":"20.8.a","level":20,"weight":8,"dims":{"new":3,"cusp":18,"eisenstein":6,"modsym":42},"old":[[2,1,4],[5,3,3],[10,1,2]],"T":[[3,1],[7,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 5, 10, 20]: [1, 3, 5, 5, 13, 24] (certified at ell = 2147483629)","T = [(3, 1), (7, 1)]; h of degree 3 = 1 x 3 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"20.8.a.a","letter":"a","dim":1,"charpoly":["712","1"],"traces":["1","0","-6","0","-125","0","-706","0","-2151","0","-3840","0","-4054","0","750","0","858","0","21044","0","4236","0","85338","0","15625","0","26028","0","-83106","0","-145564","0","23040","0","88250","0","-498886","0","24324","0","-689514","0","867890","0","268875","0","235638","0","-325107","0","-5148","0","1835442","0","480000","0","-126264","0","629508","0","-2667958","0","1518606","0","506750","0","-3373306","0","-512028","0","-2600052","0","-1628494","0","-93750","0","2711040","0","-4243528","0","4548069","0","1251378","0","-107250","0","498636","0","6299466","0","2862124","0","873384","0","-2630500","0","3976514","0","8259840","0","12505326","0","-21722638","0","-529500","0","3045918","0","-13726102","0","2993316","0","-20315238","0","-10667250","0","8720154","0","-605748","0","-4741571","0","4137084","0","-1953125","0","-14401906","0","-5207340","0","35128320","0","-14857064","0","-3253500","0","26666946","0","53710484","0","-1413828","0","15567360","0","10388250","0","1950642","0","-35791374","0","-8139220","0","-1845558","0","18195500","0","5107346","0","-11012652","0","-60248628","0","88562210","0","-2880000","0","-112169874","0","-46313601","0","-45265644","0","10375362","0","-11031250","0","-3777048","0","19153692","0","-24603970","0","16007748","0","62360750","0","-3294720","0","-18375768","0","-115012692","0","131761178","0","-3040500","0","146841546","0","127106552","0","20239836","0","58672836","0","86189250","0","-183562038","0","-80808960","0","89050064","0","15600312","0","-108486250","0","102768184","0","9770964","0","-3478332","0","-47843590","0","-33609375","0","-75106002","0","-55349674","0","-16266240","0","-288910038","0","-29454750","0","25461168","0","-97938216","0","86439854","0","-84211650","0","40638375","0","-85312376","0","-7508268","0","135897600","0","-327697920","0","643500","0","452156538","0","352213516","0","178761006","0","-60597294","0","-229430250","0","-37796796","0","-37418118","0","516074060","0","-17172744","0","-60000000","0","-78699118","0","313108164","0","53604726","0","117664922","0","15783000","0","486796884","0","-409602509","0","-23859084","0","-279303270","0","-78688500","0","-99947520","0","-345960252","0","-612730340","0","-75031956","0","333494750","0","-672856666","0","130335828","0","39315252","0","-192263686","0","-189825750","0","73161378","0","319127040","0","-18275508","0","18055752","0","-63343750","0","82356612","0","-166360428","0","-916104232","0","1073103786","0","421663250","0","-756503326","0","121891428","0","558965760","0","810946900","0","64003500","0","387175350","0","-19976050","0","-105517512","0","1364993874","0","325006500","0","3634488","0","-1099368984","0","-451021803","0","28449426","0","203561750","0","364117766","0","1483144614","0","-1295822052","0","95794898","0","11718750","0","336911724","0","-684090292","0","86411436","0","-850349142","0","-338880000","0","-1866831390","0","-128861934","0","73220004","0","-210769920","0","530441000","0","-1473826006","0","89142384","0","-1009380030","0","590116456","0","-568508625","0","1915722240","0","879404174","0","-160001676","0","-444432648","0","-156422250","0","-322262904","0","-2385600276","0","1417797746","0","-506857338","0","13406250","0","1883578348","0","-93404160","0","2474340156","0","-142266334","0","-62329500","0","1795852872","0","2807175032","0","699305157","0","-2296302462","0","-787433250","0","214748244","0","163361094","0","2647733760","0","48835320","0","-357765500","0","-3288937078","0","22332024","0","-955697610","0","-1266956158","0","-109173000","0","3939529350","0","2381554036","0","-30644076","0","-3332697600","0","328812500","0","-3948035742","0","-3235811496","0","2022483844","0","361491768","0","-497064250","0","1472387942","0","-531373260","0","-3211065600","0","-71304948","0","-1032480000","0","1835636712","0","-419097676","0","673019244","0","-3707056974","0","-1563165750","0","277881606","0","-2288929506","0","1149716764","0","547733232","0","2715329750","0","-904849920","0","-62252172","0","1900377834","0","6070400762","0","66187500","0","-124893912","0","3877748797","0","-1354071708","0","2795289756","0","-380739750","0","-114922152","0","1248410880","0","-4102611706","0","147623820","0","1715762750","0","-2538765298","0","5738777658","0","-1748882664","0","2995930768","0","-374164500","0","3193578570","0","-3518426060","0","19768320","0","3522136746","0","2539404750","0","-3210936714","0","-5350809330","0","-2591167912","0","690076152","0","1333406250","0","-350237974","0","-790567068","0","-883472868","0","-7048097280","0","-1090019250","0","-2425008162","0","-3063248816","0","-881049276","0","7578937074","0","75718500","0","-762639312","0","-3064308480","0","-8517048730","0","7255981206","0","592696375","0","-5511046234","0","-352037016","0","-955276452","0","1315742906","0","-517135500","0","-970804182","0","6965299100","0","2221177464","0","-4447422996","0","244140625","0","484853760","0","-428044188","0","1571272412","0","-534300384","0","1800238250","0","1317983778","0","5592711852","0","4197441582","0","5025311402","0","650917500","0","12804668694","0","-2417310720","0","-616609104","0","-11181660174","0","-4391040000","0","3502890594","0","4113410604","0","4558177058","0","20869992","0","1857133000","0","-7092099828","0","287061540","0","10244958720","0","-7024007278","0","406687500","0","6277312266","0","-2807418884","0","450636012","0","6991478994","0","-3333368250","0","332098044","0","-7440881868","0","-4173421672","0","-5831447040","0","-6713810500","0","-591603012","0","1733460228","0","-6738602070","0","-10498556984","0","176728500","0","-8828760156","0","-7105551706","0","9127828728","0","-12422140632","0","-1945920000","0","587629296","0","17781059544","0","15336182428","0","-518639124","0","-1298531250","0","-3272070322","0","-9441357003","0","744649620","0","-7155088366","0","-243830250","0","12953495040","0","1705585340","0","511874256","0","-9590737542","0","4473921750","0","-2691714078","0","-2150418108","0","6332489636","0","-815385600","0","1017402500","0","19593397346","0","1966187520","0","-11689142598","0","9690628012","0","230694750","0","-2552025432","0","21016805378","0","-2712939228","0","21239314650","0","-2274437500","0","-2113281096","0","-14510132616","0","9984199680","0","-2163082968","0","-638418250","0","-8336008018","0","363583764","0","14342558028","0","10815901732","0","1376581500","0","-16077520686","0","202177404","0","-13550151366","0","6253416960","0","7531078500","0","224508708","0","-1861497174","0","-25801353136","0","-3096444360","0","-11070276250","0","18263877160","0","-6156428724","0","-6636487614","0","-148105606","0","360000000","0","-20146626570","0","-19856411062","0","472194708","0","-278941806","0","14021234250","0","-3788739792","0","17107787568","0","-10343269073","0","-321628356","0","5789200125","0","3347549126","0","-705989532","0","-42573933468","0","20098264010","0","5658205500","0","-22374421854","0","-18889901356","0","-2920781304","0","16636069098","0","-1296920250","0","2457615054","0","16295147520","0","13675382524","0","-8553481614","0","1378906250","0","14229036002","0","1675819620","0","24186932622","0","32324125322","0","472131000","0","-9109441074","0","10167745636","0","-17464584960","0","4958766072","0","-2394211500","0","2075761512","0","12097241784","0","1574809236","0","3676382040","0","3075496250","0","6037848998","0","-26898956226","0","36140075412","0","-4805291520","0","-2000968500","0","-24800593920","0","14378321936","0","4037139996","0","10540610808","0","-7795093750","0","46725394338","0","-9959256618","0","-6841551708","0","-235891512","0","411840000","0","-8599299814","0","1153582116","0","-36221566458","0","-58841745732","0","2296971000","0","-3083219754","0","6601914676","0","-438968268","0","5788007562","0","14376586500","0","-1914762240","0","-18826863876","0","-6323736015","0","-6551769618","0","-16470147250","0","18201784406","0","-108334512","0","48622001016","0","-37919601704","0","380062500","0","-37874963214","0","-24189949440","0","29524845402","0","-49234566414","0","-18355193250","0","998162568","0","74063996820","0","-13347486364","0","5496625392","0","-15888319000","0","-12664143118","0","-12985004808","0"]},{"label":"20.8.a.b","letter":"b","dim":2,"charpoly":["383376","-1640","1"],"traces":["2","0","-20","0","250","0","1660","0","4858","0","3600","0","13180","0","-2500","0","5460","0","-40472","0","-97888","0","-41820","0","31250","0","-185480","0","118668","0","-115928","0","776880","0","207500","0","306940","0","-456952","0","-353148","0","1215340","0","607250","0","-2068500","0","462306","0","-4281576","0","1400460","0","450000","0","-1221040","0","-1992504","0","-1678676","0","5657900","0","1647500","0","3663940","0","-150816","0","1794936","0","5062180","0","-312500","0","-4327920","0","10178224","0","-4777502","0","-7214100","0","682500","0","-4438200","0","-15330828","0","13865768","0","-27291520","0","-5059000","0","14024020","0","-7513200","0","3351612","0","5672980","0","-12236000","0","-121980","0","23315116","0","37899752","0","-27674940","0","-5227500","0","38517260","0","42574584","0","40664858","0","-40364040","0","3906250","0","-2472980","0","-41010640","0","-46033200","0","-18959920","0","-23185000","0","32714100","0","-28310552","0","19303104","0","-5539680","0","14833500","0","-139561140","0","-46604388","0","-21711560","0","97801860","0","-14491000","0","17605900","0","107277096","0","-29589456","0","29811580","0","97110000","0","54201420","0","-26935362","0","-65791288","0","92522220","0","25937500","0","114219120","0","67446264","0","-181911620","0","348441800","0","38367500","0","-370599840","0","-189877696","0","33999096","0","-119077580","0","-57119000","0","60170220","0","39459184","0","-267578608","0","127758120","0","-44143500","0","-90200460","0","-219168000","0","-147594992","0","-186215520","0","151917500","0","159836960","0","352241528","0","188152536","0","4368580","0","75906250","0","51922500","0","-69889508","0","571651200","0","-208729020","0","-258562500","0","244504640","0","211023888","0","202820788","0","-29069660","0","57788250","0","-208183120","0","61817424","0","265662000","0","-126487440","0","-535197000","0","476274660","0","-113962168","0","353274972","0","-923171580","0","175057500","0","-246628680","0","-790903476","0","-228473960","0","-944221760","0","56250000","0","247229980","0","287426888","0","-57915708","0","-148401620","0","-152630000","0","101946840","0","1172453222","0","-159424168","0","145070940","0","-249063000","0","25428960","0","-255109224","0","1268447360","0","398936040","0","-209834500","0","-99101660","0","79590176","0","-372469656","0","1581907060","0","707237500","0","1164558300","0","-79034400","0","-665097936","0","650367120","0","205937500","0","-1660568440","0","-1704417936","0","535188256","0","-73825780","0","457992500","0","-737132540","0","464687256","0","-2769242400","0","231075320","0","-18852000","0","1617317220","0","1277504620","0","-1366030384","0","-578961180","0","224367000","0","-4156052160","0","-1401224208","0","-676115286","0","2519719420","0","632772500","0","-733978340","0","20113908","0","70846536","0","2258045980","0","-39062500","0","899076840","0","568038616","0","-225718528","0","-1095598140","0","-540990000","0","3529205660","0","-1341720228","0","152130888","0","2937177360","0","1272278000","0","-719554820","0","485162368","0","1093111140","0","260263280","0","-597187750","0","4239715680","0","2004277828","0","-397373832","0","-2502425040","0","-901762500","0","-3687000400","0","-925145352","0","1187509372","0","-4996748580","0","85312500","0","-4378196440","0","4827002400","0","787088952","0","-2202785420","0","-554775000","0","948692400","0","-4653741296","0","3821702874","0","-274079940","0","-1916353500","0","3402166440","0","-2464413612","0","-4586263200","0","-2204453920","0","1733221000","0","-119071820","0","-2374683792","0","4495748460","0","-5291906300","0","-3411440000","0","4528727220","0","5119523072","0","8451524168","0","-409539600","0","-632375000","0","976083420","0","-5096245872","0","547845128","0","1523343360","0","1753002500","0","-967631060","0","8712252560","0","2301526800","0","1845675000","0","-939150000","0","3004192320","0","2793677608","0","-3360187872","0","-3488911020","0","418951500","0","-4016149740","0","-714312852","0","575839448","0","3034787360","0","709122500","0","-3847670640","0","4653735816","0","-5476619532","0","-2256240500","0","-1529500000","0","12998490960","0","-5899346686","0","-6725673816","0","-747006600","0","-15247500","0","-10188410160","0","-11312276400","0","-1060010612","0","4699962920","0","2914389500","0","-6371500700","0","-10710604804","0","-1816092048","0","5331344000","0","4737469000","0","-510171540","0","9047951240","0","-1683396000","0","5972424300","0","-3459367500","0","377078300","0","5723011140","0","-3679190624","0","9569829120","0","-653437500","0","-7341875900","0","1141027544","0","-5894790816","0","13436180640","0","4814657500","0","2436085140","0","7467063008","0","-254114712","0","-11369166300","0","5321823000","0","-2397528160","0","5954774400","0","5828088580","0","13518494420","0","5083107250","0","2325113740","0","-8799484992","0","-13581666744","0","1582228300","0","-5045505000","0","15754966980","0","-924198440","0","3626881728","0","-9125154600","0","488281250","0","-17184127680","0","-18335616936","0","19031560504","0","-3099751600","0","-309122500","0","7904367420","0","7725222744","0","-14941323756","0","4282644700","0","-5126330000","0","-15196668180","0","4899960000","0","-20500755968","0","8898531420","0","-5754150000","0","4238768660","0","-14982503112","0","-2739285764","0","-30624962160","0","-2369990000","0","-2276502120","0","7844908160","0","26827336800","0","-2665683020","0","-2898125000","0","12914236620","0","11812592312","0","23764995984","0","-6120503220","0","4089262500","0","-1473120280","0","4862890344","0","-3217686464","0","-21079957680","0","-3538819000","0","19579009320","0","16203113976","0","8719648140","0","-13585685200","0","2412888000","0","-1110231480","0","-9806085572","0","17797168496","0","4216454880","0","-692460000","0","27229851840","0","1058783568","0","3481693616","0","16494075800","0","1854187500","0","4320818620","0","-14742030086","0","16823066520","0","-13784144660","0","-17445142500","0","-14189436720","0","12596530360","0","-2052151328","0","-11934012300","0","-5825548500","0","-17316577380","0","5895616224","0","-5634810008","0","-17950957200","0","-2713945000","0","-17936087300","0","-16756675200","0","12705520404","0","32198301800","0","12225232500","0","-16525188240","0","-25301062364","0","-10556304936","0","-21572320020","0","-1811375000","0","22668748480","0","15047496528","0","-11913069600","0","-12442442160","0","2200737500","0","3923708020","0","8285604768","0","-24661640904","0","-23002056280","0","13409637000","0","4874121660","0","-5000277672","0","-29239842012","0","45369623520","0","-3698682000","0","23022099720","0","-8624425548","0","-15226410992","0","29629209920","0","3726447500","0","-19399317040","0","49791232072","0","14343579612","0","1104120580","0","12138750000","0","-22726546620","0","-35479631444","0","23123015336","0","64413116820","0","6775177500","0","-1824090880","0","30351583776","0","-26288158306","0","81930561720","0","-3366920250","0","7414520140","0","-12949724944","0","-8999171976","0","-20586867380","0","-8223911000","0","4345047540","0","-32512265432","0","-23099402688","0","-48828088140","0","11565277500","0","-34803821180","0","49486622400","0","32459176088","0","34448023940","0","3242187500","0","-7988441780","0","-75409783320","0","-40044567276","0","5296792780","0","14277390000","0","256029660","0","201461552","0","-52023553200","0","42106907280","0","8430783000","0","5600205120","0","3363816048","0","-52936577928","0","-86032261760","0","-22738952500","0","2079137140","0","-507977652","0","2432715144","0","-13914501840","0","43555225000","0","-60499164240","0","14102074912","0","83108072912","0","17886210000","0","4795937500","0","11053268900","0","25775883924","0","14933630184","0","-35128528800","0","-46324980000","0","21857581540","0","-39332112328","0","54227375244","0","10149742440","0","-23734712000","0","-14288293980","0","18856686392","0","-34605541176","0","28195314900","0","4249887000","0","43169029920","0","27784798488","0","41314442370","0","13030065300","0","-14884697500","0","53910482140","0","74595090336","0","-5054550528","0","12233195120","0","-7139875000","0","-17694133740","0","-63589816800","0","85180762364","0","-61668076860","0","7521277500","0","99969319680","0","-23594753280","0","48250077832","0","-97939727440","0","4932398000","0","62414074060","0","-10357250416","0"]}],"seconds":0.261,"computed":"atlas","estimate":{"seconds":0.405,"low":0.247,"high":0.7,"bytes":1853261}}