{"label":"28.10.a","level":28,"weight":10,"dims":{"new":4,"cusp":33,"eisenstein":6,"modsym":72},"old":[[2,1,4],[4,1,2],[7,5,3],[14,4,2]],"T":[[3,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 7, 14, 28]: [1, 3, 6, 7, 20, 39] (certified at ell = 2147483647)","T = [(3, 1), (5, 1)]; h of degree 4 = 1 x 4 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"28.10.a.a","letter":"a","dim":2,"charpoly":["-697020","-1372","1"],"traces":["2","0","-224","0","1596","0","4802","0","22210","0","-50592","0","-184772","0","-507144","0","-152124","0","-605024","0","-537824","0","-2503608","0","322886","0","-6251840","0","-2727492","0","-6655040","0","11796288","0","3831996","0","-6860228","0","42039944","0","14154756","0","-1133840","0","91283388","0","35486640","0","11529602","0","-93958608","0","-33311940","0","-95542272","0","-8752648","0","29419488","0","35951692","0","53326210","0","-339557376","0","-170286704","0","300326544","0","-463615488","0","-100806860","0","-560276864","0","-121471392","0","-197493824","0","865463530","0","51427488","0","877573512","0","239581776","0","649287492","0","-443637572","0","2359082768","0","205828872","0","2781293620","0","-1934940576","0","-116857524","0","-759283280","0","-1217652744","0","-2839054368","0","1119156940","0","4414153520","0","-1383373812","0","-2177181216","0","-6833280580","0","-365249724","0","-2406282838","0","592782000","0","1857498216","0","-2717867528","0","4375068992","0","-1403005632","0","-1452662624","0","-10410720240","0","-795479916","0","13819501696","0","-6466123248","0","8260033152","0","-1583462664","0","-1291315424","0","-16060167636","0","20785476568","0","23173878084","0","-19834186512","0","15310208956","0","21492565920","0","-6011162808","0","-3686996192","0","23899465728","0","6666612288","0","8348453046","0","10420643744","0","-37278456516","0","775249286","0","-34617340008","0","3800478864","0","-6005138468","0","-25086040072","0","-38286733800","0","-14799282624","0","-15010667840","0","-8675637552","0","7067502460","0","85402942464","0","-48830164452","0","3118729936","0","-949949392","0","-6548708292","0","-8307536760","0","-32265195192","0","2450110656","0","11651723824","0","53003811840","0","-39137514528","0","-15978751040","0","84223604384","0","-50878822296","0","27588258544","0","120987102598","0","-83676919872","0","3312394540","0","28322887488","0","50744471316","0","50742914832","0","-15055979680","0","-37730347896","0","130594427572","0","5469091936","0","9200622396","0","11134275704","0","64305947928","0","-34920785088","0","66678239232","0","-161885284848","0","98727805092","0","-16471407428","0","-15527797188","0","-101248265856","0","-186437585880","0","-128752193568","0","-89587214052","0","105995367184","0","100937905544","0","-96218814432","0","-70172143796","0","-435377115712","0","76315195380","0","-29622337472","0","15230448912","0","33985569156","0","112046443526","0","-256181998768","0","-367953322548","0","305377967592","0","259352580480","0","242952960768","0","-2722349840","0","173519466264","0","218224505328","0","-139462310624","0","-17256350992","0","125533218384","0","37528314628","0","219171414588","0","145602407628","0","57923886528","0","282869203344","0","278778987600","0","-336436620716","0","-58373969584","0","85203422640","0","144343813744","0","-892843820356","0","44309752368","0","122628838684","0","-259694250816","0","439450564224","0","27682574402","0","670824828864","0","235824504624","0","-899262140756","0","929996365040","0","68958097908","0","-379675054080","0","-225594617808","0","286153500840","0","-301895715678","0","-40624472672","0","-736842998856","0","-498643000688","0","-330709121148","0","-79981967940","0","-69607534292","0","-37908443184","0","213432139032","0","-471892104752","0","-286776026320","0","-404170786320","0","-229396995072","0","-964160969488","0","26926590300","0","129825344880","0","-894064003848","0","176977520160","0","-332615561012","0","-21015107848","0","1332920848908","0","1558857723920","0","876525531756","0","786032068800","0","226480284436","0","615031052832","0","70636190688","0","-589553303832","0","-1088831083768","0","723027576768","0","-492217304756","0","952201920432","0","1569794313612","0","86320012492","0","-2031403676928","0","2172816738840","0","1150853973892","0","572605027056","0","715594089840","0","-872976588512","0","128036230210","0","-1465369338672","0","1022419368792","0","1512385767648","0","-469844027388","0","7864557120","0","-2043301516144","0","-815277259776","0","-1687456489844","0","-1357024694880","0","1344049209804","0","-1718095603760","0","4601907031008","0","-1354916819424","0","-408858376304","0","-3069431007352","0","742358873856","0","1001389396672","0","-4348533909060","0","-2752057477344","0","2766586694648","0","721084032144","0","1721566328712","0","-409593635288","0","1175464543232","0","349646812080","0","407918168280","0","-4017512733696","0","-1113140786688","0","6505262752","0","2217288489264","0","-560788484256","0","-1537135116336","0","-4879073771712","0","557501955276","0","-242037270860","0","627988424720","0","314756647728","0","-1316262132864","0","4579627601832","0","2899937809524","0","1253388904768","0","-1345224750464","0","-4402735379616","0","-457401157486","0","7342911461088","0","-33504204696","0","-1949621412816","0","-2743423570608","0","-291652812192","0","5866551024124","0","4159382982248","0","290342768856","0","-1427158807520","0","5116560466892","0","963285756720","0","-474182671424","0","8323890953520","0","-1886894280276","0","2589877105760","0","3999028173696","0","-6465790241568","0","2627756757864","0","2077977935530","0","-3439405323684","0","2578145232496","0","-5697377257152","0","-690356029416","0","-314528263532","0","-112364178304","0","123477398688","0","3826612445760","0","-14382228323328","0","-8381661038016","0","-1370737789456","0","2622532608192","0","-3354396844764","0","2107054002312","0","-527592934960","0","-2500637963760","0","-4887745846172","0","2593907645840","0","870939650028","0","-388947687296","0","575235844176","0","-4736066170320","0","-56741084852","0","344425309200","0","-1290732342132","0","-2779416555776","0","8154997935840","0","1558939268292","0","-679535355454","0","-193274173824","0","-10568745225192","0","7267750234384","0","1989203630960","0","3151736417760","0","-1065173810372","0","-5390118483456","0","-2863429069332","0","462724622752","0","7959540591552","0","-9175764354288","0","-6006351403584","0","5664157725968","0","7315102124220","0","8341207217352","0","-17456505058636","0","1420595122656","0","9168855826732","0","14329370476848","0","494195121672","0","3378305454480","0","1802617280192","0","-4447421696256","0","-8168757803612","0","-9662431869440","0","14597764810524","0","6677885981620","0","16522032075768","0","-3900011779104","0","-5368228693128","0","5062663672424","0","13468109643240","0","5393084502400","0","-4645792322976","0","6897384397752","0","-7702463883096","0","-4150584418176","0","2887178466780","0","-5569958049712","0","-13498283217888","0","-280574915124","0","5969621786908","0","6134095589312","0","9211895877408","0","16548026130432","0","4822870133424","0","-9121070387856","0","-1823039155280","0","-15936176255920","0","506214728436","0","-3959818330496","0","-11402068310054","0","-12836413912224","0","1743754937932","0","-2923584238344","0","943866344064","0","-6805698306272","0","-635356892912","0","1453214337864","0","-10238836705272","0","-15123642900576","0","-6816569537568","0","-4582412905352","0","-21204730633464","0","14024763566016","0","-4962841894580","0","-15645459529728","0","5365938163908","0","2687095812940","0","23991193387656","0","-21041527869288","0","355213803700","0","-18852398321856","0","4376252554716","0","-24253859111552","0","10598382601520","0","-8849490014256","0","11908868751360","0","7437956907360","0","24409735185408","0","11475179699872","0","387069123840","0","-3321480522612","0","-15641211599392","0","40524476573520","0","36558337609500","0","4880321914176","0","19761504358596","0","14802793989312","0","-5227412099616","0","3438464660328","0","1211927400588","0","12123955943680","0","-40962994120096","0","-9804911688768","0","-8565221272384","0","-16406706672580","0","-4878877245876","0","6182907192544","0","25024128658368","0","6376676073696","0","25238020664332","0","-18508177902592","0","-876964587324","0","-21355584983856","0","47445611571680","0","9861257168112","0","-25175675072338","0","17355533987904","0","42158488805748","0","-5777485094038","0","-31944659751784","0","10578272010576","0","-13712613522356","0","-6289725673464","0","28540315483764","0","-22371444320288","0","1423269582000","0","-17863426713936","0","-33388172548128","0","4336029282592","0","-1249644606720","0","4019202195344","0","18493939035572","0","4459853216616","0","-18153559947092","0","52086583279800","0","23932239991380","0","10556415564832","0","-64028135788848","0","23765889620928","0","-6525599934728","0","-25362630638112","0","-5510208205584","0","23892711574032","0","-55771644132864","0","6161408951712","0","-51497101542600","0","10504540649792","0","-36173367761952","0","8834796298096","0","-37234341685044","0","-27923534910168","0","10470149129664","0","-47149710169632","0","-3368616522432","0","8009634979552","0","-21466683411208","0","43462723627008","0","-53475921671180","0","14482480726448","0","7255504162116","0","-3487842960224","0","-11821971551232","0","-32883404212224","0","34221835462612","0","65117639202032","0","-6594487137252","0","-16529729568912","0","-24996139296240","0","-13006251499680","0","51979085665400","0","-1792084381248","0","48324325569876","0","53098279200288","0","-13180277642112","0","-1909947278316","0","40633839384546","0","-23664204321312","0","-472897911864","0","40292823445192","0","8174434873584","0","41533196703936","0","33180623572096","0","89547741853784","0","-24012532590012","0","-25837751467584","0","-2573402305204","0","-12878564443248","0","-13348458938808","0","-15525161918448","0","3738796533312","0","-53110557942272","0","46520039451200","0","4093403128080","0","-48467222609540","0","81636813725600","0"],"derived":{"al":[[2,null],[7,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"28.10.a.b","letter":"b","dim":2,"charpoly":["-3933036","-1484","1"],"traces":["2","0","-70","0","1554","0","-4802","0","-14498","0","62388","0","122766","0","371552","0","73584","0","1171198","0","168070","0","2262384","0","5394106","0","315980","0","-1923360","0","2977884","0","1896496","0","-3731154","0","-13418528","0","-6247176","0","-36367800","0","-21964916","0","-41080886","0","-1362732","0","11529602","0","-69515588","0","-17898612","0","125996920","0","4270012","0","224710542","0","-85847118","0","34809698","0","58332228","0","179568872","0","87785824","0","231378168","0","88098332","0","473120158","0","-149793588","0","-184274184","0","-274532642","0","624641094","0","-1214688044","0","-490397404","0","-1574777148","0","-294761166","0","-1140879096","0","1769997744","0","213665984","0","-737855932","0","-1205841966","0","-416388476","0","-892096352","0","151924896","0","225950360","0","3521231476","0","-123809016","0","4930288384","0","-753405114","0","-176675184","0","-2027190278","0","1607394396","0","13732427604","0","-4239627096","0","1948541728","0","-51871218","0","-2812046398","0","-10182395584","0","6659243724","0","6013866866","0","-3716510760","0","3474595992","0","-12091035796","0","-403536070","0","-6194688012","0","2767471304","0","4152399944","0","-17382594096","0","1421109886","0","-15116364900","0","-5431983984","0","-31692478676","0","12047161600","0","29190602700","0","-13503571526","0","-11658350242","0","24785543958","0","-12951248506","0","-863570644","0","28969162992","0","27989297070","0","-26473518864","0","47553880668","0","-9887727640","0","-758667980","0","13213677000","0","17750921248","0","22588535424","0","38909403828","0","-7021325444","0","-39883394824","0","4617987360","0","-21901874076","0","-28087870096","0","44772023856","0","3648568216","0","-7413410816","0","5348883960","0","-7149899484","0","-2741522284","0","10340599548","0","-3020536904","0","-85435845154","0","-17331906018","0","-59165549002","0","-4553486896","0","-35626066812","0","-72578763984","0","-57434978160","0","33502520496","0","-54508142864","0","57028084190","0","8958500754","0","67953857880","0","-109216798196","0","-51852755598","0","100961212544","0","6172844608","0","99787858548","0","32217885728","0","52982486920","0","141909010296","0","-313020731604","0","102043813188","0","79519185270","0","-454902000","0","14999469576","0","288732066540","0","142216089100","0","50979039804","0","-79937899884","0","-65421534514","0","222649817152","0","87319087800","0","-34585168538","0","-68813284900","0","-181476542310","0","307624759328","0","-90031740512","0","124345591104","0","52737763316","0","-96372779296","0","-626788402572","0","-382526608114","0","174132232072","0","-293662103616","0","-38698403800","0","98635207286","0","369742112676","0","-161501422568","0","-416696369544","0","-92061441996","0","273519902082","0","-115898144908","0","3271919532","0","-63039044372","0","-116339900248","0","-498846188232","0","198416464080","0","-49407248548","0","-95778760896","0","-27682574402","0","438997207552","0","-106882810788","0","379982462006","0","67144660752","0","-368061656508","0","192792512752","0","166906926788","0","-347982883608","0","131860842942","0","325499441218","0","74948871348","0","137709032104","0","240213684480","0","42974567412","0","1178123443124","0","350542289472","0","-69540401532","0","390903271460","0","550421944800","0","66388053396","0","-302518604920","0","76639799324","0","536586370608","0","-415332590176","0","-267533123236","0","-1356987958368","0","934544528694","0","-10252298812","0","-1313380453632","0","272980278144","0","805826782306","0","136810542840","0","806215520320","0","-1250977795564","0","-539530011342","0","-1174386708176","0","-322535413852","0","812825577858","0","-2227790778852","0","273372890868","0","-1778014861896","0","206118930318","0","67996728384","0","122391864384","0","770698683160","0","-419778207808","0","1661960752032","0","-849225878256","0","-83578084898","0","-1701419766936","0","-331996196844","0","1802855746860","0","-1875239185548","0","-1073574259128","0","1013588936528","0","-140055679428","0","-251978051632","0","1650454239496","0","-153801109602","0","1581413915840","0","437114224512","0","1137143111958","0","-431144861672","0","-1487941760840","0","-470455510128","0","4495187178986","0","1231744180788","0","1168733541948","0","-1089157224876","0","-210773763424","0","-999346064172","0","4303919197552","0","1037483595568","0","-1020745890312","0","1594572740824","0","-2065345439080","0","-555538981368","0","319495927592","0","-1799244670312","0","2568352455816","0","-3569906921596","0","233186371054","0","1118513321142","0","-211524095132","0","-923065292024","0","2708080226976","0","-727594623168","0","1009155412520","0","851907434616","0","-334959621626","0","-1135961499358","0","3205008631944","0","200472437074","0","-2119017601778","0","-2261468028852","0","-7698155321304","0","42036232392","0","359654404788","0","-1481148557196","0","-2479971008280","0","-1876244334132","0","-1343805025596","0","2685777517962","0","-2252344285716","0","442442315784","0","-2151063162176","0","-122808751980","0","-1450912399944","0","-1591946353120","0","-3070601650662","0","-1117270323484","0","659152873442","0","3947021781408","0","-4770209257932","0","-1773672632592","0","11031704043216","0","7435363742996","0","-139161318548","0","-1499763266694","0","-3423521872968","0","-2146961759052","0","5993733190746","0","-349156829448","0","-5885923484756","0","7792441794396","0","2916465993644","0","5143885474840","0","3140757394944","0","-3876802140092","0","1050199148152","0","3261281002266","0","2699995985568","0","1177444167004","0","243837376704","0","-1737540182256","0","-6718798016448","0","8164756552608","0","-6049858286962","0","-3730307473088","0","3781039932348","0","15927100823686","0","2234168609312","0","-9605721308232","0","-2062042339928","0","11199836453176","0","4344474678768","0","707721559566","0","-1725198094312","0","-10131076662384","0","-9707912746406","0","-3948420032000","0","-1605224438244","0","8283856942480","0","2739250709496","0","654668034456","0","-5157927637840","0","-662559162188","0","8289259747380","0","-5771694186454","0","-4542665954736","0","-4249764583344","0","-6329550794912","0","-962657538128","0","-8042941573800","0","3437190609580","0","-15352760509436","0","4789014034014","0","-513012027584","0","-382311863652","0","6002516002728","0","-14165948665708","0","47238040760","0","270954519444","0","-2484389794082","0","1771592092732","0","2543823157584","0","-2336924986056","0","-4865487179420","0","-8233688400120","0","-1696730509348","0","-674754014592","0","2895226560366","0","8814079620496","0","5807723781816","0","-4352434148160","0","6302305259760","0","-827745215472","0","10009912782828","0","999748730876","0","12045827417116","0","-21654497066184","0","13339470849236","0","9255814039666","0","-4330925418120","0","-6516755771358","0","2141923341152","0","-513452750160","0","6700885823340","0","-742203619248","0","4405123349496","0","25321519077036","0","1586781903014","0","-364771675296","0","-3227606636256","0","1946453848164","0","23248883414400","0","-7195132298784","0","6290146112768","0","1938977311824","0","-542506814360","0","11349160216196","0","13184294245224","0","8597887874408","0","11624308292820","0","-8142218607558","0","-22576710108204","0","-8454476773876","0","-20621548613676","0","7342248734240","0","13350107081528","0","-26221653000348","0","5244759349158","0","1716230491584","0","297265447416","0","-2704953028716","0","-5088327970752","0","-2570725919706","0","11189782614936","0","8130696635292","0","2810368687560","0","-11837622409984","0","-16201365377752","0","-26448480608352","0","3490523473430","0","-29300680794720","0","-25988365935000","0","-10480677884992","0","1808925678714","0","-39359743451844","0","14259134069696","0","21546300085520","0","-2004794041728","0","10126666444706","0","6308883718396","0","424197116784","0","7907200357472","0","25849818458352","0","11669634161556","0","-13289801237426","0","-10108664105372","0","-15041609090466","0","4867283857478","0","-5501823348724","0","7549258628832","0","14972690046454","0","-32752695319696","0","-1959846997920","0","-36793057014350","0","-3859353944796","0","-14507646004200","0","54914707225316","0","-3715242951602","0","-17375241472896","0","13945544204424","0","2744583564184","0","-32971558677204","0","-19597633386544","0","24921678936720","0","31693494965244","0","1525064941600","0","42529971063104","0","18032100709476","0","10179344657496","0","1198504208372","0","-8397947177688","0","42572221449912","0","3690740227200","0","22926085729848","0","46349523798816","0","-4678448688928","0","-6758882782380","0","-18881832433584","0","18441555778954","0","9481651850760","0","3586560783344","0","-19249889008896","0","124542794418","0","-18140194921216","0","13997195728124","0","14143106305776","0","53910558341912","0","-8150704416316","0","-2143671065760","0","6751723401598","0","37243687344560","0","-44505083966160","0","-10100854633604","0","-29161785181252","0","3347616940962","0","-38647449060192","0","24447931797184","0","-26761127249148","0","5377992930924","0","-6028045311204","0","-6721598498364","0","-14645657785248","0","-15668539532576","0","-15988844181324","0","-508432522862","0","27695226301776","0","22952763387204","0","-72122236747040","0","-34312655888728","0","55393648009854","0","-14439294345266","0","25796821915176","0","-76169278683492","0","-40582954787256","0","5921377601920","0","-12431826506316","0","-55725185890388","0","8923342334760","0","-16059612772608","0","-4826499811376","0","-32139610585376","0","87609072731712","0","-27761297170166","0","-76828848146792","0"],"derived":{"al":[[2,null],[7,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.317,"computed":"atlas","estimate":{"seconds":0.499,"low":0.304,"high":0.863,"bytes":1891000},"url":"https://sagebrush.space/atlas/mf/28.10.a"}