{"label":"79.6.a","level":79,"weight":6,"dims":{"new":33,"cusp":33,"eisenstein":2,"modsym":68},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 79]: [1, 35] (certified at ell = 2147483053)","T = [(2, 1), (3, 1)]; h of degree 33 = 1 x 33 (phi(ord eps) x dim S_k^new); 6 primes, 0 rejected"],"newforms":[{"label":"79.6.a.a","letter":"a","dim":14,"charpoly":["-188859596097536","-5920808092928","63423242231488","-12781417798336","-1521265929888","411504328944","13321554304","-4743555482","-69043350","24302749","320017","-55232","-956","45","1"],"traces":["14","-8","-37","192","-201","-159","-157","-474","213","-419","-566","-2153","-651","-2811","-1633","1668","-4864","-1067","-2736","-14249","-6089","-19094","-6182","-23643","-3373","-19667","-16477","-10841","-20034","-4887","-7238","-10826","1164","-22782","-19167","12959","3944","31414","-3567","53905","-53860","67615","16800","7960","13962","91078","-17691","12975","7169","35379","51246","123365","-4126","39393","6894","-61063","982","155532","-37693","192039","-83846","121970","-8732","231980","-30311","316232","4252","-44566","-52140","267735","-128821","417279","29398","52294","45920","109442","48944","163311","-87374","-291941","-172122","-82458","-223066","137633","-59212","93250","-174722","-483536","-493717","-184292","-344099","-92810","-326932","-8611","-421784","-306195","-272397","-13671","-593612","64999","-440463","428356","-205171","-610129","-377285","-16562","-117597","-314045","-110576","592986","-91702","265295","-667004","-153110","-126382","-621532","-335118","725663","-101782","771633","295512","230764","336306","257472","-594615","69066","86625","-467218","-584996","992941","-383870","1372244","-87492","-88588","856679","-289070","-474110","-62478","78653","-500743","177175","-8539","593034","481355","655678","22492","976080","648266","-390680","1289074","262346","924338","-214318","594176","624426","1214497","48402","49928","570832","1612721","-785482","659164","1793824","-1783474","-359514","463778","756934","1882455","1194315","1183896","1611388","1274262","-729896","-353080","2771660","-748384","937593","2530117","-574248","357712","-581238","-1840683","2532740","1977622","-2148830","-1282988","1955446","-2926593","478021","-1541064","-2159189","-1550121","-1038658","-3456945","1426583","-941045","-1281574","-1115238","482983","-4842965","-987254","-2655151","672634","1687984","1959772","-4553435","1167916","175373","-4747244","-2618259","961440","-1007106","2193099","-478521","-1767294","-1892643","-1949384","-1451098","1058116","-2855696","-1947316","-349610","3562614","-4874447","-2436273","560060","-846968","-2866510","734662","-5914484","704654","3926492","-4579834","-2153498","3436869","-6831951","230917","-753760","1023108","2002127","-328233","-1725008","5235722","-7682152","-2305082","3424768","1633204","2495136","403938","2170695","-718181","-5514310","410948","-4914185","3394306","2545892","-1926994","-1256252","6016286","-3864307","2527032","-1394318","3119886","9027156","-966724","-3490998","5052279","4191800","-539685","4479375","2733342","-2600718","878669","13850","4959528","-5679354","2536313","5780145","6270780","10758823","-5096867","5014663","4142412","-4443041","5040722","-1973304","1792734","14296567","138738","-3562340","6120875","873520","2587450","1972008","7032117","-3569602","1249458","677772","800106","1791210","-1639024","4945952","13230017","-2385378","5256622","-5497278","1372960","16001188","4340759","-2218826","-3091180","1836695","5564634","8189728","6151734","-1198272","-5023265","1720906","-3831876","-11885677","-6663107","-847190","1150666","2555924","-5038082","-3974730","2499650","-3109266","-4210253","-4615392","-4840682","-4128410","-1358550","-2607918","6257696","3607025","-3677623","5314701","-952040","886864","-11782738","-3260564","4213579","13378702","-8503320","1417866","-4361666","-2619276","-5305078","-3050768","1023465","-23548256","-12100400","-4328309","976447","-1289567","-13481798","13454882","95731","-21309056","-7806860","428778","-4009747","3428023","-8031888","3626672","-4893594","9753746","-14087998","1763546","687668","-10389664","-6439254","12537768","-7517589","1077169","-21627102","4995157","4548849","6109218","-12869107","-1747121","-3683790","5129717","-19602824","-4810960","12803716","16374721","-12429591","-2329495","-16301094","-1886013","5689848","-3083606","1254441","-35200316","-12045385","19220897","-5095160","10394875","-16155906","-22523276","11380182","1186881","-8667693","-1073376","-272938","28240632","-12157410","20287836","-1367252","-7223597","2986101","15326564","6660738","-13943593","-13242797","13216510","-4104617","1381343","-957523","720382","5167518","-3268798","-6691552","10012079","-12484032","36676657","-16827132","-10477200","10523968","-6648453","-5155797","8910588","11371654","-10553630","-7032458","10543330","82360","64942308","-12464605","17787628","9904148","-8014718","6870791","20608526","7294238","24908887","-726216","6467319","13378090","-12484268","11264624","-4975958","14964929","-20128826","-8065999","18887386","12090138","3615486","-2550524","-28410592","25308191","-1344004","-4255066","33412502","17490994","-5477260","-12205276","16523779","-3597550","8281275","-11584196","992319","8464536","33619508","-7007530","-19379666","4649248","20929241","-27856252","12975649","36484598","48167868","-2430911","-9320058","10864850","27825096","-15184018","-12744688","11984761","12225364","4549544","28995748","30357708","-4898312","8986539","11063170","9676910","22392915","-1317568","3643045","24233101","-1317682","-5328327","-23475014","9075792","-3816327","-9957190","-17000304","-12543158","-17972314","-20340956","-40709870","24992083","-52382788","-10214086","21190682","14679884","11830247","-18731190","-12413940","9650570","-795030","17849324","-43409776","-14817154","30474068","-9005264","35144174","-13518802","-31983106","21754948","-62363221","-21785527","23545252","-48549116","4658093","1708208","9325257","-7192025","33512484","-793596","-53022462","17373230","-37682213","-7599862","-8136710","-31507362","-18364558","6079268","-53520702","979837","-15974169","5618258","-72421569","-19223141","3296750","-6580008","-20277607","-31486756","-38543887","9891918","-20033735","8756082","8281392","4434163","-45906167","-19442234","-26782090","-11271966","35479480","42119985","4791092","23861624","-47979189","-8740690","61728388","12619634","25149252","-19422238","-38382789","23258078","-14206168","15518110","-55262274","9274927","20316052","7269808","-36579673","-26851222","-33409430","8628477","11890952","19307986","-8532432","-4081637","-14269800","30158020","14250618","5196376","5371488","46577256","-27099096","-7568639","-23812189","12583263","61454714","-3787102","-44186176","-164413","-89792458","28395132","-17692290","15667606","-56590644","-6918677","18651","8747697","22419932","1421394","-33048164","-20201637","50044793","2182124","-28952186","45905272","-30766468","16953640","-8655522","1706421","2958234","28619324","-1837305","32974793","-59113350","22164866","88780776","-55411156","49904041","-17207031","-48600593","6878516","-33641726","67869920","-56380460","-15998860","-24456246","-10772294","-9442456","26503534","37501336","6921267","-21855538","56278882","-43943978","43142904","57060233","19414391","-82309468","21848462","35975646","9009778","-13012350","38354982","39832","23344424","64968704","20034310","-30615082","-10525784","29056207","73587056","84244493","-14623492","-13574437","69421825","56010082","28523321","62798472","-31016576","-47186288","36265912","91789744","81301726","21484787","19752504","-9529906","-54592674","97605918","-26649981","27542430","44770538","-20841726","-763079","-38872804","42101368","51041352","920358","63023972","-5802192","-15911319","46552240","100350464","21460535","-23306110","3702837","50274625","24265032","44414371","-1329333","45020683","41460240","-23431376","-36819686","22832762","80889806","24677655","-35022218","37744804","42116975","-21009382","-32702513","-38078620","5570888","-131099107","-42584978","45654001","-58363602","-29063140","-77693068","63234232","50122246","97918926","-23775808","48389998","-62364312","-43603622","-33170687","7157330","38377536","-139847346","-10905796","-38383464","-13505916","40982850","-30564460","146193008","-27125563","-55713501","-73021246","-109320985","29419919","9691208","-8194662","61804043","82732967","13718171","-14047284","-105564434","-121096402","101392209","15304674","-59148339","9470198","-73676284","-116157067","-59879649","38803264","24755044","-59573368","-75904604","-30433338","-8509238","-54267748","-140348681","20850306","-16837903","-117134666","-91306461","55621322","-3014980","-84734","-10266457","-35267896","-82740122","-8683290","-5288978","-7789620","2614979","-101501980","-13608620","47401928","-30923593","9433232","-19720449","-28317530","110574738","-21651850","-92114061","-77199118","-72840968","-99039524","14906636","34797404","-59007884","-39449433","-146662989","-30195087","65896909","-59080166","-31969932","66394128","-38046164","-97540152","116605224","45803050","57128336","340048","85398532","-52516482","-48380184","-6541804","-45102539","61497700","97527553","-65118253","57227728","-45133880","55106874","11660465","49289189","-43112574","136766833","-1582390","-207619748","115598066","53422183","-20213436","-31473607","33603018","-102950849","-52488863","-60655470","-103116102","-76286006","-69349969","261175958","11120410","-120087434","-124429092","157275721","62116554","105457088","-82361492","87445595","-126629709","61949432","-13186639","39029684","80997214","-13401978","-74281670","-76411995","49206490","141147911","-57605351","-69824400","3532406","55925216","-15793952","93815598","-71589442","185059998","-88860383","6751806","43320414","-95673250","50422412","-159968100","-161021744","-3622941","95048109","5215440","-71476395","18658986","-198750538","78655022","54211725","-39937055","80109310","154296586","17130760","134414292","28733172","-66767207","-40104178","-33070682","-114807644","-142038765","123885668","171405416","112263156","256158912","8361230","-1661768","-58786380","59559842","31253118","262358787","-26737168","-77422830","56376772","160409683","-28125516","218759910","14174250","139819912","-82407260","-8600750","164255508","32148154","-48059685","-129302548","160188128","-135635761","4956662","189589948","-221028182","89075644","52204900","-99932206","106650268","-75790400","-10463516","34277576","113819618","53113560","-30216164","180673841","-47492784","51310548","-23022586","-100423823","94457161","27328912","-159079344","13436873","162413290","84689162","134439023","35161996","-35676209","246762020","-12481925","180662730","134786912","49380386","-97944212","-38257161","-57884736","-72497202","28822734","75024541","120769038","-86811190","-23616852","86333214","-47290068","245491553","-89396034","22812598","209439491","68654534","-41105156","-462474904","-25210036","-17235572","-196804106","27818188","181693094","78360083","-22386962","355995044","-4026184","-42246848","-42695355","-55921430","52378486","-25469454","73239961","148962704","54825316","-51992335","119778501","-16791074","-56840146","-22037338","2199746","265170953"]},{"label":"79.6.a.b","letter":"b","dim":19,"charpoly":["-60090647579363652243456","-15428410480253436636672","3730518629110530777472","1168489366510480801856","-21276571156911119904","-21960253942720551712","-454950677654686656","187607222495222040","6058750661275016","-904085700208615","-30831667632887","2692793282610","81870294760","-5086486233","-118699364","5911257","87572","-3796","-25","1"],"traces":["19","8","17","352","199","201","39","294","2238","381","1370","439","701","1893","167","6788","4962","2821","1596","11256","14607","22553","9674","32023","19780","23544","11297","9459","11496","8083","8502","3491","24782","-20150","211","22039","-12080","24290","-2607","-47010","42270","-114653","1674","1844","5606","-46410","15351","-122399","55794","-65616","-52494","-146939","4306","-113401","-10962","8929","-41612","-219754","28691","-247041","-57770","-39231","-108750","47988","48241","-273612","-106648","28320","96754","-331737","4263","-478785","83698","-42310","-1462","-431997","151166","-417363","118579","95175","264475","-91454","398834","261517","283542","-70034","91266","251504","597611","25380","449613","78289","683070","-219091","402096","750237","204743","20841","814712","-27305","476309","-387036","549439","797631","596299","-55458","125511","-31623","177060","649771","529766","-664319","416208","-869806","98622","46164","-233058","593491","581526","-59945","532775","-47598","109974","273464","553605","-868996","-334995","-591262","257324","-586344","526174","247110","-366692","122796","-572839","-1228030","301408","-1754246","-101711","-895523","-396809","-1384267","94630","-86205","-9366","808316","-1178528","-1436918","-18808","-1442988","-935582","575197","121536","-1897300","-115506","-689447","-408992","49928","-2461220","-2335767","605562","-873064","-95848","-72852","-1701890","-1043078","410238","-4483121","339148","248538","-1039432","-1056466","-732266","-2376340","-1845708","-1010355","154421","-72892","-916704","214333","440822","2501191","-4301504","1024923","3569934","1236992","-2527628","7579967","2409901","1497795","131965","-3182633","-1163050","5028963","-2103143","2928879","1220276","4345373","548335","5721767","2147432","1314432","1138526","1298208","-2731110","5683563","-545108","-2491220","5996392","164493","-1356710","5057950","-38833","1788071","-1133112","4882567","-703394","7964318","-5191654","1153209","3083514","2321886","-4762054","10485625","-4427776","1040722","400038","2020392","-1204122","8078841","-4759354","-3162736","1644026","6347233","-1635477","1903495","106097","-3226952","-424744","-4265675","376875","6636524","-7207482","-4361468","2556338","5788736","-1995084","5622560","-1425014","1187076","3242905","-5588008","-3753468","504805","-9033018","1901892","6403062","-4549512","-8930350","-657396","4550742","473778","1787514","-3807146","358164","1356752","-6404077","-316293","6794335","-260443","-8543460","1268100","-6262739","-347380","-3674272","2926080","-476139","1797245","136236","-3368787","-644931","8570283","-2594140","-1630747","-847764","-5501292","-307862","-15596140","-479615","-4004002","-2240057","2547631","-886642","-7009666","-11353323","-4337634","630578","-5456872","-6374274","-4786822","796828","3378812","-15477375","-19192514","6559920","-5276438","-4317250","2839792","514271","-8215269","1211328","-14807993","-7500370","-4747976","-15270598","2196832","3568405","-2856086","-4973132","-8191053","11571045","-5420292","-15028352","4133564","13006448","479221","339882","-1197134","9828367","-5726868","-4317902","7334778","11058882","2788453","6364260","19159465","6502213","-11001923","4768764","3499164","13231760","23109056","2630157","-2499044","15381314","10839288","7852734","-9197476","10800154","-9123338","745287","9902996","189556","-2805605","-6782253","17008737","31925766","-3546534","-5815067","-9969479","30686643","-3346429","-9327471","22326617","10737746","10601680","-2505526","-14299126","5277952","15558168","4525616","29397042","-1169572","-1203496","2280413","-2424383","13038430","-14224127","-10639485","-9341926","27355941","18207331","-16545162","26662181","1953606","-12188490","15669142","13394408","6516889","-13671301","2063076","-14187585","15376686","-1941810","1241959","-2547568","32543997","-38296577","-30495228","2983736","12021682","1981996","-17978810","4239301","25298463","4109144","-8220140","-976436","8044548","-31570766","8474472","13892869","4673589","-16466828","5447130","26833163","21562307","-3862009","1041095","2331887","12624349","4185058","2520210","-8076902","12348836","6767991","-11032612","-24360163","-9458462","-1563618","-8336204","-20031235","-151969","-44540152","-17579906","17781836","9476716","-15723170","-12992076","-12077049","30468392","20313176","-17115326","-1999786","19010163","11874258","-2941102","-45955477","28841634","-903492","12631196","-4819850","-5619194","-21018604","-11982103","-31776250","-3514299","-39851912","-21047902","-2203398","10628312","-3648748","-9463311","-52849550","2768670","22624776","10128658","-89354724","-4452768","-74463083","-7419866","45905491","-18361224","1254441","-20919648","3187384","-6667102","-42743678","1795396","-3512191","-8670742","-15138708","-26719750","-10027687","-2765237","-12791700","1962914","-60818446","-9856172","-10043400","8032955","14071012","91168","-61431129","-2826804","1175689","937823","-36420558","2567034","14601636","12128002","8634259","-7489633","46335816","12087489","-5951231","27047218","-26127489","11985326","-175220","-12182074","-41918334","-8294556","46134073","-7986205","76206664","-10527490","-54475202","23657740","26091738","52203292","32733982","-14870982","37457509","-4994380","74795791","-6796356","47264698","6397939","-10135316","-23752612","62536228","-5303450","55834753","-21689307","-1685859","8389008","11146317","13455896","36071179","-10871287","19620428","-60206770","52390700","21937026","145853939","-18013738","-33873162","825666","-53539","25940480","-6215942","243399","-49839309","29427418","26293315","-44280825","53573081","-4908656","-56485453","11736668","46349361","-8056498","-12733679","-13726560","46881797","-25805337","-16327699","24078522","55191794","25997442","31973121","-634647","47693380","-2310744","100451031","-9020224","-31660412","20307102","2870094","-5214142","64130345","-25334008","3723739","-43880346","100402056","-16287341","12665250","755680","-7038023","3179882","-21230876","15032769","23859760","-7851258","-36650998","-24230037","48067629","18539856","31421180","38121204","-52294612","-16742528","93471805","-3274029","66205513","22577409","-85835778","32116614","-17284200","-10953899","37256940","-55539252","19286220","-16065878","1223498","-17005665","-25970197","15887095","-101696095","41585646","-29337962","-67001577","138107305","26917297","20732923","-56218160","19015858","-30078304","9595004","-8954791","1834854","10921596","52085907","-29507455","-65720282","-58414758","-41923156","-19135262","-2827230","22870469","41091415","-14941740","-54289260","-83918428","24809206","-5304288","-118075682","35556650","-109068093","-7191962","34293376","-28024173","58629222","-44700942","48837528","8521600","25754729","-18616447","17489440","-2801812","-41000668","-67561302","-44362150","613988","16106060","-13957884","-103976440","-57854938","41244723","-28628312","-13059861","17024210","22317629","-14972880","42158232","30951431","-67090066","-15128349","-66336170","-741752","34366744","-28971952","-27126967","-104192412","-24258467","-27937268","-23673134","27093236","20446498","-41397117","-98853122","-138844180","-3491794","-60476981","63853868","-36187588","-46676744","-41516818","7493094","-27889120","-23685637","3264128","-78464501","-58708165","-23219872","-64841459","55044209","-12061204","-63505931","13967358","-10995745","-11277324","23870896","-59420562","68158838","-34665652","-88819927","44969186","-39427644","-5462401","-831645","-28595797","99167220","9182782","10345385","3458222","-104919655","-41566257","24482355","155174332","-84300212","10864746","8723747","-18401942","28807662","84101912","32772038","-93148671","36476278","-114816700","29442426","47475608","108075210","54063066","96615234","152561084","-96404404","19285685","-97147815","35787210","212759871","-17021453","8611188","103486842","136513427","-121238291","102806837","83600644","32963946","47275518","83012553","35056366","14192421","-56465668","9380673","119018219","-134104839","58209024","-99907666","-23621338","-1083582","46286110","-54460138","44306316","33413238","86990282","-144558624","153806816","21092537","-86087426","50411002","-68631542","-14961165","106973582","148501438","122592494","-165744796","-111153438","2377821","194471504","78274540","74362736","-6135373","-8192048","84195157","-98672596","47034506","7512558","127131532","88190790","-90518774","85946620","-14155266","-87545718","-156792460","156220639","-118013697","87452661","130997721","-54116218","162759108","-57882640","13620906","225930292","13904176","53002840","-178311950","101263158","-87036312","3196494","104015856","1905588","117661657","8594464","74828617","122923177","11543963","-37086382","-13650442","30042073","27491200","64198840","-97571115","82168026","200930255","-74267998","-114142131","144936856","-161838275","60956117","107946715","110423733","-210007154","-16304740","-172687932","-137627945","123160952","-42886304","51392314","122979348","94469209","-155074154","9824944","-40593844","139223041","167901419","-102394848","15790675","-140059360","-108211606","-17868290","109819842","72680827","-146401092","-31688237","14320267","-9410364","8550170","22272512","48993960","194103148","-47899050","-55708179","213170005","-223537636","-12653314","-49302770","27609160","-131704545","143178792","-99161513","22868229","-23999980","-152482255","-41626096","83494970","-166471330","44855461","-128914916","186643314","-93997586","-166312956","30187412","47465832","159339693","-298961650","52155906","74985692","-403465653","-94268756","1505200","107812252","-2198672","197791706","160834208","56609116","-113972108","-116962394","-155398881","143563564","132434562","149071708","-79356652","-50113956","-46103768","-64960810","-330311872","-48531848","337460190","5219340","168441436","-39693323","-461059224","-226701374","-191626097","185313746","-198090760","91123328","-214658536","134287848","-50872544","-122634004","-173626915","127611052","81807172","-202929660","-245205198","-83936074","70739445","-81368614","127004012","-43352772","-205228107","91470025","-270684524","61936510","2739799","-15880510","-141017989","76054421","-136848508","-62406933","-108020516","-31293267","16615175","-287838204","-80613526","8952188","-400897567","-3480029","57419892","-60489776","-419992019","-106974950","-336792238","-23128268","45646995","-88766840","156753684","125706774","-94299820","-75837925","-95721639","120293120","-98768534","50530330","-50424568","-171441878","3891837","-148116318","126127761","208124568","145351024","61071546","-54219976","-81099257","102715331","139277936","372357163","-190104305","300769252","156083916","20679173","187116063","9756318","-57827138","-105349701","235754334","207252426"]}],"seconds":0.246,"computed":"atlas","estimate":{"seconds":0.462,"low":0.282,"high":0.8,"bytes":2068162}}