Properties

Label 1.80.a
Level 1
Weight 80
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 80 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{80}(\Gamma_0(1))\).

Total New Old
Modular forms 7 7 0
Cusp forms 6 6 0
Eisenstein series 1 1 0

Trace form

\(6q \) \(\mathstrut -\mathstrut 16086577320q^{2} \) \(\mathstrut +\mathstrut 1942174928281180680q^{3} \) \(\mathstrut +\mathstrut 1549737362258405903681088q^{4} \) \(\mathstrut +\mathstrut 6092984858773763455723827540q^{5} \) \(\mathstrut -\mathstrut 2227106590325939088404927087328q^{6} \) \(\mathstrut -\mathstrut 204133057837186288371299604423600q^{7} \) \(\mathstrut +\mathstrut 542570064661378776298915601390568960q^{8} \) \(\mathstrut +\mathstrut 98496326492153316059886441015309696222q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 16086577320q^{2} \) \(\mathstrut +\mathstrut 1942174928281180680q^{3} \) \(\mathstrut +\mathstrut 1549737362258405903681088q^{4} \) \(\mathstrut +\mathstrut 6092984858773763455723827540q^{5} \) \(\mathstrut -\mathstrut 2227106590325939088404927087328q^{6} \) \(\mathstrut -\mathstrut 204133057837186288371299604423600q^{7} \) \(\mathstrut +\mathstrut 542570064661378776298915601390568960q^{8} \) \(\mathstrut +\mathstrut 98496326492153316059886441015309696222q^{9} \) \(\mathstrut +\mathstrut 2720626696366658228219065452729623532240q^{10} \) \(\mathstrut +\mathstrut 326182707503353434196853598345012484552152q^{11} \) \(\mathstrut +\mathstrut 3662741799314627362069151990938777789858560q^{12} \) \(\mathstrut -\mathstrut 249286867791526696387831019648013646893106140q^{13} \) \(\mathstrut +\mathstrut 1866634067474695788912841823339193553138295616q^{14} \) \(\mathstrut +\mathstrut 53939724989186019570794541522119517534771796080q^{15} \) \(\mathstrut -\mathstrut 681627631644510368706137880459644753465449181184q^{16} \) \(\mathstrut +\mathstrut 829554518710324966978506506427078451803483469740q^{17} \) \(\mathstrut +\mathstrut 20783419681388619276512545895581772264264550807480q^{18} \) \(\mathstrut -\mathstrut 50727940848110344442361931427855575819428647228760q^{19} \) \(\mathstrut -\mathstrut 1467030065046629207751264576643706806587735144958080q^{20} \) \(\mathstrut +\mathstrut 11440846038310308150487768012211089482880511198926272q^{21} \) \(\mathstrut +\mathstrut 36817507512313772519930542191150104222671820963556960q^{22} \) \(\mathstrut -\mathstrut 1046924887201563380993656359631631933258453525094738960q^{23} \) \(\mathstrut +\mathstrut 4647998047182641817986339484942489649049309172966328320q^{24} \) \(\mathstrut +\mathstrut 10836995626543537474051791335153252813979338793331307850q^{25} \) \(\mathstrut -\mathstrut 165657588130323625805363235243378873928973276983585168368q^{26} \) \(\mathstrut +\mathstrut 452244485424938477892504860024752019079362449583874943440q^{27} \) \(\mathstrut +\mathstrut 1004680642640065837930850364413184139977872155405489282560q^{28} \) \(\mathstrut -\mathstrut 7120822866262655112931363073018274881104708247497947521340q^{29} \) \(\mathstrut -\mathstrut 1093089132342530488188112356341250721972394415479943059520q^{30} \) \(\mathstrut +\mathstrut 134345039550847531062964315804153164343444264343589333172032q^{31} \) \(\mathstrut -\mathstrut 367680407387361126658464447414461787802285956837455133573120q^{32} \) \(\mathstrut +\mathstrut 694937277679484430969386562214930563011269531321798125315360q^{33} \) \(\mathstrut +\mathstrut 3154306959722239121253159757854043021326472297974364404980016q^{34} \) \(\mathstrut +\mathstrut 9191056770903655504272784196241783249847740561191433159558240q^{35} \) \(\mathstrut +\mathstrut 19880287065959074647932230862843896929437344679866234828597056q^{36} \) \(\mathstrut +\mathstrut 200218543091040103155222783880989961642213560574664429550198420q^{37} \) \(\mathstrut +\mathstrut 866365883974611161836395390925862263352921297032838009795060640q^{38} \) \(\mathstrut +\mathstrut 1846928010477803855453412626793191219191424716227436821180804144q^{39} \) \(\mathstrut +\mathstrut 9116669264447274408945009430906339427674431802850195585057510400q^{40} \) \(\mathstrut +\mathstrut 19216804901837266991242147464997667315402616992351385711235458972q^{41} \) \(\mathstrut +\mathstrut 112315174478490788723912174839938916243710780267342081630678531840q^{42} \) \(\mathstrut +\mathstrut 108832931910908864051094641347526853298463718485111641638401400600q^{43} \) \(\mathstrut +\mathstrut 495514650695382135238363336424200091081783038631873261666636656896q^{44} \) \(\mathstrut +\mathstrut 1089311173064980984859644147008913582964905804089164802662670706980q^{45} \) \(\mathstrut +\mathstrut 2339423217798161589056888023635021837153755261863446723443331974592q^{46} \) \(\mathstrut +\mathstrut 766732507168785220421816169748850175208159379232549271592508353760q^{47} \) \(\mathstrut -\mathstrut 1227537570851109157458973684400646232156423736031048093315900456960q^{48} \) \(\mathstrut +\mathstrut 3801016219812200810689187746878210669081675204402752707309154018358q^{49} \) \(\mathstrut -\mathstrut 50723521315108078882353551947661611720805543300108849711322864485400q^{50} \) \(\mathstrut -\mathstrut 139865466375558864334882784640098531626186142446280524443365433199728q^{51} \) \(\mathstrut -\mathstrut 279692249004488191323071540832092417841619330373410063262542264310400q^{52} \) \(\mathstrut -\mathstrut 312193237964710957330604375297544855480450344577449082153802391971020q^{53} \) \(\mathstrut -\mathstrut 996221038973994559873624494431619704350011373216284617130312268666560q^{54} \) \(\mathstrut -\mathstrut 861958222068919393142591787960630586871784969446963670182827020790320q^{55} \) \(\mathstrut +\mathstrut 1123629643438673418216699268533992018915072902064015953839024305295360q^{56} \) \(\mathstrut +\mathstrut 7795598779799587371741461301046795526293245245773998812837273820000480q^{57} \) \(\mathstrut +\mathstrut 16584702356914156466182151363602691995360915944935914137385742159510160q^{58} \) \(\mathstrut +\mathstrut 24289171784532714189639095038219795042285164994033400426178461238907320q^{59} \) \(\mathstrut +\mathstrut 73025956047571458013400417312791668535879728806786116560639243534051840q^{60} \) \(\mathstrut +\mathstrut 80560570425826852880081093564684385117241348668836108242495308815618052q^{61} \) \(\mathstrut +\mathstrut 59777568713863815377707698536571620658579394379949737090862924510332160q^{62} \) \(\mathstrut -\mathstrut 276708678056196744256455115102015383166989187390931876478468368856762480q^{63} \) \(\mathstrut -\mathstrut 719203226636338274682481908236724651863342420498670194455988567598170112q^{64} \) \(\mathstrut -\mathstrut 1007462919483461647300380829039677154191109543250817689988654733030592520q^{65} \) \(\mathstrut -\mathstrut 3347562853423538991999694027669961627986534585541581689746575315495214976q^{66} \) \(\mathstrut -\mathstrut 1851521876973893932513297183455714100127257334040085257904842903903517560q^{67} \) \(\mathstrut -\mathstrut 5899582938115809421316043854246769288699297144820927766700932855979726720q^{68} \) \(\mathstrut -\mathstrut 1427672735602453311144050658084524391331260046448660152415370050225171136q^{69} \) \(\mathstrut +\mathstrut 31159148342952686307596185437939815723517531766889921556924090292621741440q^{70} \) \(\mathstrut +\mathstrut 38507401093845789827495210229167852070939724868887506542264571604541264592q^{71} \) \(\mathstrut +\mathstrut 87904411000641647434917578390462554629488250565124366592415232306933521920q^{72} \) \(\mathstrut +\mathstrut 61123654206386061400310438862981106227383729069503080628162601940159787740q^{73} \) \(\mathstrut +\mathstrut 136513352063977853606694381822259496818965955504365628093794971441921163216q^{74} \) \(\mathstrut +\mathstrut 113188706706427317048365034543759604727098826077328333023878456326260918200q^{75} \) \(\mathstrut -\mathstrut 249903768766885839664688587580825575582546834454828556400015599314274074880q^{76} \) \(\mathstrut -\mathstrut 1195099252106099653800449972868194220235362175583181442486256041652274244800q^{77} \) \(\mathstrut -\mathstrut 3022231856978250782599441544561070134871217051487771942772538597436408443200q^{78} \) \(\mathstrut -\mathstrut 188234723479363903277484397100590307076741783512190126828886315155446684640q^{79} \) \(\mathstrut -\mathstrut 2750248132852209015421484068233717972689944891189322073844459755369097666560q^{80} \) \(\mathstrut -\mathstrut 4202996734890713231427597758184507891641102417282671988811370042535012566794q^{81} \) \(\mathstrut +\mathstrut 3834792966214046709977047126406184257851543195738078433637414913324683717360q^{82} \) \(\mathstrut +\mathstrut 14506845760765784842493952470927474286413727909244314121162679395439622145320q^{83} \) \(\mathstrut +\mathstrut 48942789227023150657016145376829988370028655394086238910889917134273615865856q^{84} \) \(\mathstrut +\mathstrut 38946066828627954832778050727572362568084538101228336437758435671222134267240q^{85} \) \(\mathstrut +\mathstrut 66363633323077708072616297459993363454350669286030390599179655949306835458912q^{86} \) \(\mathstrut -\mathstrut 12188467007600920252987005731487987332580129454574096199578444638747687628880q^{87} \) \(\mathstrut -\mathstrut 68086553439664359269830684533538140843829745277114000504065479672707840583680q^{88} \) \(\mathstrut +\mathstrut 88790169947368466670673875396871954428202115924137373286785364937730407494780q^{89} \) \(\mathstrut -\mathstrut 678121360108159288271315537216087664710338266311311066150921870820864233179120q^{90} \) \(\mathstrut -\mathstrut 1105665330428280782729905276805137770501582996765091919549546053816493845198368q^{91} \) \(\mathstrut -\mathstrut 581852119074779563003978084378550280950528927013853021971971412987670782543360q^{92} \) \(\mathstrut -\mathstrut 724063571132401087495277238269757837179269218308363767014177350097338957840640q^{93} \) \(\mathstrut -\mathstrut 342394004508386413823498343959337212855421843329465021317054652742559913721984q^{94} \) \(\mathstrut +\mathstrut 4133010515441143062055572903340407460351722715065934937506390604234109634359600q^{95} \) \(\mathstrut +\mathstrut 4500277093535091993817003185543220432802869972147132801867826645045331188908032q^{96} \) \(\mathstrut +\mathstrut 2053881285944963905800936410853289740689894385863240159901124624782493905690060q^{97} \) \(\mathstrut +\mathstrut 21591608457226642856925919189308208713047358263642522360137695155926522503830040q^{98} \) \(\mathstrut +\mathstrut 12210721611676619111412804269965201185505307365258823385190308559518832844781624q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{80}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.80.a.a \(6\) \(39.524\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-16086577320\) \(19\!\cdots\!80\) \(60\!\cdots\!40\) \(-2\!\cdots\!00\) \(+\) \(q+(-2681096220+\beta _{1})q^{2}+\cdots\)