Properties

Label 1.82
Level 1
Weight 82
Dimension 6
Nonzero newspaces 1
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 82 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{82}(\Gamma_1(1))\).

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

Trace form

\(6q \) \(\mathstrut -\mathstrut 460872026640q^{2} \) \(\mathstrut -\mathstrut 15648291925893129960q^{3} \) \(\mathstrut +\mathstrut 4493950976700073762513152q^{4} \) \(\mathstrut -\mathstrut 18364304155649862126617790300q^{5} \) \(\mathstrut +\mathstrut 79543552376002656592687080272832q^{6} \) \(\mathstrut -\mathstrut 31430760593927655842892725138869200q^{7} \) \(\mathstrut -\mathstrut 5498145101596630185016447889074360320q^{8} \) \(\mathstrut +\mathstrut 1187896030123132129876714384590115355598q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 460872026640q^{2} \) \(\mathstrut -\mathstrut 15648291925893129960q^{3} \) \(\mathstrut +\mathstrut 4493950976700073762513152q^{4} \) \(\mathstrut -\mathstrut 18364304155649862126617790300q^{5} \) \(\mathstrut +\mathstrut 79543552376002656592687080272832q^{6} \) \(\mathstrut -\mathstrut 31430760593927655842892725138869200q^{7} \) \(\mathstrut -\mathstrut 5498145101596630185016447889074360320q^{8} \) \(\mathstrut +\mathstrut 1187896030123132129876714384590115355598q^{9} \) \(\mathstrut -\mathstrut 66472312087527710620452553569669697173600q^{10} \) \(\mathstrut -\mathstrut 2302475295973581620809306061775551681990328q^{11} \) \(\mathstrut -\mathstrut 53870867926220164150329513348046663235681280q^{12} \) \(\mathstrut +\mathstrut 1313253814255449492724146018729804193778100180q^{13} \) \(\mathstrut +\mathstrut 41225372723246048337281629784765672712004401024q^{14} \) \(\mathstrut -\mathstrut 156056001993392003275961063842210281482861266800q^{15} \) \(\mathstrut +\mathstrut 2799490233261278434402974316306719898117729222656q^{16} \) \(\mathstrut +\mathstrut 2377848571505238562780180385684069414829577769580q^{17} \) \(\mathstrut +\mathstrut 506306622204276540508620731115428014111485052430640q^{18} \) \(\mathstrut -\mathstrut 17422016964741760630179674590582970665727618619375240q^{19} \) \(\mathstrut +\mathstrut 148672889698640611477740875719636714144962866333222400q^{20} \) \(\mathstrut -\mathstrut 114072752249915469711576730788399479267919883382138688q^{21} \) \(\mathstrut -\mathstrut 1258034178625689345497738618244246726621220713529586880q^{22} \) \(\mathstrut +\mathstrut 10526595063181453314046018770874462030150898790798283920q^{23} \) \(\mathstrut -\mathstrut 12327611736558023893782629055720670133074337356786974720q^{24} \) \(\mathstrut +\mathstrut 411037910011361515508644334216291479522821661187695496250q^{25} \) \(\mathstrut -\mathstrut 3180570114716540139250277986112641638356676984048903123168q^{26} \) \(\mathstrut +\mathstrut 14621431460046183096199709161966291993457773283863231280880q^{27} \) \(\mathstrut -\mathstrut 82116517748637002885903417761702653442063276903193852344320q^{28} \) \(\mathstrut +\mathstrut 155464359052154485146727469597467543970919715236853926245940q^{29} \) \(\mathstrut +\mathstrut 164012983787559943750248070451087782537372525868704541558400q^{30} \) \(\mathstrut +\mathstrut 1259277021063335018777245090979655984137503836933555134668992q^{31} \) \(\mathstrut -\mathstrut 13036312845125683749178794475020758767431562303480221102243840q^{32} \) \(\mathstrut +\mathstrut 21091354949357251433966784004957297352147245536782330440814880q^{33} \) \(\mathstrut +\mathstrut 11899550405754031112224464347628728246396477955985557631122144q^{34} \) \(\mathstrut -\mathstrut 232034356615504837711196063040035766391492406317925929510437600q^{35} \) \(\mathstrut -\mathstrut 2071479648832132808682929357240066191852277967275841354377712384q^{36} \) \(\mathstrut +\mathstrut 414692688584236378963319357622814947056491742931883680122973540q^{37} \) \(\mathstrut -\mathstrut 2455417714037465297201999851134772037590829998762172946918415680q^{38} \) \(\mathstrut -\mathstrut 92285563929532296901251298670288831485071753513924535804838199984q^{39} \) \(\mathstrut -\mathstrut 258059824285668605758122263287555971608050642150708772544789504000q^{40} \) \(\mathstrut -\mathstrut 250252788823194090638944408016236187978548863949167831014660870148q^{41} \) \(\mathstrut -\mathstrut 3774470339882908627686770098374833879180889302300694800640098910720q^{42} \) \(\mathstrut -\mathstrut 5362516930786214192203446564720631507618558180640993338648106782200q^{43} \) \(\mathstrut -\mathstrut 17252465656682175267213991915222412585785021276568609411813835518976q^{44} \) \(\mathstrut -\mathstrut 62055994195911488597384173133359170181530078929941731114719230089900q^{45} \) \(\mathstrut -\mathstrut 123763409427226200113215389587151615608344054530127843046255996688768q^{46} \) \(\mathstrut -\mathstrut 230717394511751791462615349254196337530205542984846694602934639341280q^{47} \) \(\mathstrut -\mathstrut 691982889190309031684460851104240936972943285356349640319551063982080q^{48} \) \(\mathstrut -\mathstrut 148965540042877735285285650175007198234557699456949204802064464556458q^{49} \) \(\mathstrut -\mathstrut 1416105420952806525015169807922957339416756851287952031511031347670000q^{50} \) \(\mathstrut +\mathstrut 723978686772453055369497103847414979467127084371963703072714225585072q^{51} \) \(\mathstrut +\mathstrut 12562371185881747636341658298037576485393840750032566447999727917043200q^{52} \) \(\mathstrut +\mathstrut 25898990256961205776642859216859182171010424056472082121008236344959940q^{53} \) \(\mathstrut +\mathstrut 60731909939285801872082597253734783721512219559188195805336458971800960q^{54} \) \(\mathstrut +\mathstrut 70427859302095658379065386305135120838252257009889309990749877277396400q^{55} \) \(\mathstrut +\mathstrut 350275852246953465289512615368698332984392220622408793911163576939151360q^{56} \) \(\mathstrut +\mathstrut 303622382725256536236947985463289143154200643659779472092208351796091360q^{57} \) \(\mathstrut -\mathstrut 312514134877257928766126367534026770462807935435519457753987287493386720q^{58} \) \(\mathstrut -\mathstrut 38532453307459913471042984274454520116124717672121643571528434328282520q^{59} \) \(\mathstrut -\mathstrut 5854438714408546634435977504160054633094179506942282108438463374797465600q^{60} \) \(\mathstrut -\mathstrut 4585192544270629640163935422584783189092178505653567017169797728495170828q^{61} \) \(\mathstrut -\mathstrut 11745445982868867354760701788812677993661414140303262885466836339630318080q^{62} \) \(\mathstrut -\mathstrut 35632339418998518169074915366562958999484559616578607415025802007025188240q^{63} \) \(\mathstrut -\mathstrut 24049189879736877632355406073912155582619770074517134096672197458230509568q^{64} \) \(\mathstrut +\mathstrut 40108571425620140080303901416556158312567794172295521521551039993118238200q^{65} \) \(\mathstrut +\mathstrut 46637466443959380664183766096173047575934541297502070623350605582042365184q^{66} \) \(\mathstrut +\mathstrut 278606964486964374833906544600580027758780739521508130980859112605565987480q^{67} \) \(\mathstrut +\mathstrut 591059149620766869951154898169335214276013402788475417448362648514550551040q^{68} \) \(\mathstrut +\mathstrut 783789679110178241786835392836945981604400905715238386162022702382323722816q^{69} \) \(\mathstrut +\mathstrut 2635837114104224632390936486964777102611174135296488988531978806621369068800q^{70} \) \(\mathstrut -\mathstrut 554281436103188717611008447226924711986842423491780222553301787426789861968q^{71} \) \(\mathstrut -\mathstrut 3169897304032072056282604590226317130165389286798806197352424269626436341760q^{72} \) \(\mathstrut -\mathstrut 1159677538409433721867557656635958525415325708297922475676033828300683142980q^{73} \) \(\mathstrut -\mathstrut 14870996314347354169518203977127998385153668929299472477677600807989626002016q^{74} \) \(\mathstrut -\mathstrut 40272209656064989140640078595938035284494253817756477276130430269166782335000q^{75} \) \(\mathstrut -\mathstrut 56365824164857229782022127848008365902008884166434980738114640515976798612480q^{76} \) \(\mathstrut -\mathstrut 22951272837324694774527636903423616359482790364245898655274441101674154673600q^{77} \) \(\mathstrut +\mathstrut 29994870322699852265351947769035786178441787146653937638111333726813935158400q^{78} \) \(\mathstrut +\mathstrut 76488528596848273963909721387433081359345259080220208993600380062891411190240q^{79} \) \(\mathstrut +\mathstrut 326185463863660018876021371340485226979224823762794013840530768719064527667200q^{80} \) \(\mathstrut +\mathstrut 713659220427214109967671419496287178348529210497808359051350032218775138774486q^{81} \) \(\mathstrut +\mathstrut 836977463852743303549437738986542975894462808796250502348000478828556860551520q^{82} \) \(\mathstrut +\mathstrut 440718478462773776637617020819789880594300172591745821478345102532528865997560q^{83} \) \(\mathstrut +\mathstrut 2327207348086698397722806131221331490656683214148360655124465557042000906952704q^{84} \) \(\mathstrut +\mathstrut 1165607138975709364402518400492567424057357396402879557680723771041190675179400q^{85} \) \(\mathstrut -\mathstrut 10339197506820945136003281093027314178240703830345630490304599234644673765234368q^{86} \) \(\mathstrut -\mathstrut 13777097629225807302706950021773234863450868385225572161845501405567814463584560q^{87} \) \(\mathstrut -\mathstrut 9603847126452588175246186358824265187739652448840879006569656469218022549667840q^{88} \) \(\mathstrut -\mathstrut 18886228493337874501351816155449414708824427288664596668607356717228138798590180q^{89} \) \(\mathstrut -\mathstrut 27536035459180423419106541648329015873635894588277179325118018321007646877848800q^{90} \) \(\mathstrut -\mathstrut 14576226325987997036142564032100430704897317032265698214767987870608618538920288q^{91} \) \(\mathstrut +\mathstrut 66364414655655668275929797141498084164407535259475789695165805684452941775738880q^{92} \) \(\mathstrut +\mathstrut 130065128543178746783515152749840115744191801626425494555088565985583783043572480q^{93} \) \(\mathstrut +\mathstrut 331286952814608158700187065887753978184064043063622410298763861434514546852072704q^{94} \) \(\mathstrut +\mathstrut 267699559747800180626411366716842325842865933645649558098598518850783266973922000q^{95} \) \(\mathstrut +\mathstrut 495554087106091786297185708372687557293322071836937974888325742175573190348111872q^{96} \) \(\mathstrut +\mathstrut 113832498161281214584608062040287314379413598012089688107897449655058469975263820q^{97} \) \(\mathstrut -\mathstrut 858118355318723523117883130491863373979750018711838274840266757637744872892872080q^{98} \) \(\mathstrut -\mathstrut 630632406390824053363198011181718527371969259570962092705191903378628178893256024q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{82}^{\mathrm{new}}(\Gamma_1(1))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1.82.a \(\chi_{1}(1, \cdot)\) 1.82.a.a 6 1