Properties

Label 3.66.a
Level 3
Weight 66
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 2
Sturm bound 22
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 66 \)
Character orbit: \([\chi]\) = 3.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(22\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{66}(\Gamma_0(3))\).

Total New Old
Modular forms 23 11 12
Cusp forms 21 11 10
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(3\)Dim.
\(+\)\(5\)
\(-\)\(6\)

Trace form

\(11q \) \(\mathstrut +\mathstrut 3624451998q^{2} \) \(\mathstrut +\mathstrut 1853020188851841q^{3} \) \(\mathstrut +\mathstrut 182297552527310043284q^{4} \) \(\mathstrut -\mathstrut 51169986413727134695494q^{5} \) \(\mathstrut +\mathstrut 16301970916583221148237766q^{6} \) \(\mathstrut +\mathstrut 7045353328705962403513562128q^{7} \) \(\mathstrut +\mathstrut 541385166531412015722258480840q^{8} \) \(\mathstrut +\mathstrut 37770522023217637331236339982091q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(11q \) \(\mathstrut +\mathstrut 3624451998q^{2} \) \(\mathstrut +\mathstrut 1853020188851841q^{3} \) \(\mathstrut +\mathstrut 182297552527310043284q^{4} \) \(\mathstrut -\mathstrut 51169986413727134695494q^{5} \) \(\mathstrut +\mathstrut 16301970916583221148237766q^{6} \) \(\mathstrut +\mathstrut 7045353328705962403513562128q^{7} \) \(\mathstrut +\mathstrut 541385166531412015722258480840q^{8} \) \(\mathstrut +\mathstrut 37770522023217637331236339982091q^{9} \) \(\mathstrut +\mathstrut 619438979330879307901236008580564q^{10} \) \(\mathstrut +\mathstrut 102779711445945907142926706248476q^{11} \) \(\mathstrut +\mathstrut 712037078029045459308073879334772q^{12} \) \(\mathstrut +\mathstrut 2236803413364017652432096558025062154q^{13} \) \(\mathstrut -\mathstrut 73111611730347705398280846705393926640q^{14} \) \(\mathstrut +\mathstrut 225109105168650616306993446179603443854q^{15} \) \(\mathstrut +\mathstrut 8817209428494398737767550388646103253264q^{16} \) \(\mathstrut -\mathstrut 27609328203731450230952135670799573996362q^{17} \) \(\mathstrut +\mathstrut 12445222182959469819458085478027000833438q^{18} \) \(\mathstrut +\mathstrut 1065990310826627973682259321160159414012964q^{19} \) \(\mathstrut +\mathstrut 246794839789344647728935680687316114866424q^{20} \) \(\mathstrut -\mathstrut 8171282585963302364950263465218503870918320q^{21} \) \(\mathstrut -\mathstrut 28668791923198331709444352896329603161079544q^{22} \) \(\mathstrut -\mathstrut 182492217093463660457127832766047149369557976q^{23} \) \(\mathstrut +\mathstrut 1638080104783332686130517758253203702575980872q^{24} \) \(\mathstrut +\mathstrut 6033734467104240936011911951865076088470091061q^{25} \) \(\mathstrut +\mathstrut 31812883785035805790949474374544042440107416292q^{26} \) \(\mathstrut +\mathstrut 6362685441135942358474828762538534230890216321q^{27} \) \(\mathstrut +\mathstrut 556953666945918751121810394028515640552302262816q^{28} \) \(\mathstrut +\mathstrut 837406052539935135744172735690636063803312665778q^{29} \) \(\mathstrut +\mathstrut 3593435577263205095009874222016368333438517446276q^{30} \) \(\mathstrut +\mathstrut 6204942990396592055727778050910347502994230809160q^{31} \) \(\mathstrut +\mathstrut 52223294277213143793777144293463538847496097862688q^{32} \) \(\mathstrut -\mathstrut 8791769474212247803686864706545373515889094737548q^{33} \) \(\mathstrut -\mathstrut 91042367601556570993107311981868509595349326151332q^{34} \) \(\mathstrut -\mathstrut 777717848664297055678304731493335836504718134510240q^{35} \) \(\mathstrut +\mathstrut 625952156591948913784578682387396529311104090438804q^{36} \) \(\mathstrut -\mathstrut 3141739618754499413856358770196284438399889685346302q^{37} \) \(\mathstrut -\mathstrut 6036614145839925099522178576851323348170126849961160q^{38} \) \(\mathstrut -\mathstrut 582888262261790931525868963652868241702547875866978q^{39} \) \(\mathstrut +\mathstrut 55889769356959167054720226735842263678164045891513008q^{40} \) \(\mathstrut +\mathstrut 12739729951808557040333109565287405814454862195173790q^{41} \) \(\mathstrut +\mathstrut 49759175555747646731387174274294407611543691714547984q^{42} \) \(\mathstrut +\mathstrut 488348829152958981907302960450395602350600910421253724q^{43} \) \(\mathstrut +\mathstrut 1353835521295621066666731060932648717843803788705961584q^{44} \) \(\mathstrut -\mathstrut 175701554433402548164666079535853072383364345154399814q^{45} \) \(\mathstrut -\mathstrut 1960542575626780874460909785920341300847951270875860400q^{46} \) \(\mathstrut -\mathstrut 7121352319512304228172058661585475634385416202818544032q^{47} \) \(\mathstrut -\mathstrut 2167508118662845627875366822767497672417459021495793904q^{48} \) \(\mathstrut -\mathstrut 14427664230896531569596301522586539803698431635048906957q^{49} \) \(\mathstrut +\mathstrut 26585117828425717813350370495953938065014718041165430434q^{50} \) \(\mathstrut +\mathstrut 1872571932086963348975911047525363531370172169946045218q^{51} \) \(\mathstrut +\mathstrut 224886220990849588873263317315551932575854906960392734488q^{52} \) \(\mathstrut -\mathstrut 73989886727661987770599374209738466246244722776741359206q^{53} \) \(\mathstrut +\mathstrut 55975813775150906157815590158898102007884377461149986246q^{54} \) \(\mathstrut +\mathstrut 848690418695216601906395846388209087315543992709228756616q^{55} \) \(\mathstrut -\mathstrut 3295458519956774021732553139133002042499380606708800323520q^{56} \) \(\mathstrut +\mathstrut 101163866345173506390137105609484277569000222432861398220q^{57} \) \(\mathstrut -\mathstrut 6915715744259737287549218415974213227802833552600845354780q^{58} \) \(\mathstrut -\mathstrut 7639459059287158667102529626062912052811345721535049084804q^{59} \) \(\mathstrut +\mathstrut 9323693921270020616909687748877565839309632216825322581816q^{60} \) \(\mathstrut +\mathstrut 20784670286902374573417399043999449740619353745336993639658q^{61} \) \(\mathstrut +\mathstrut 2914477655747437816778316389121165029970249184821991512096q^{62} \) \(\mathstrut +\mathstrut 24191515733021658449945058268692810547135628632437012349968q^{63} \) \(\mathstrut +\mathstrut 247086266702509679164429313956979051704551077507033417248832q^{64} \) \(\mathstrut +\mathstrut 613646632848692467005291059549724741527365282614998711628q^{65} \) \(\mathstrut +\mathstrut 457407027308075804282008685417539963697083291754632659195816q^{66} \) \(\mathstrut -\mathstrut 12897879862433232313348670441517039750540926988445462820732q^{67} \) \(\mathstrut -\mathstrut 3885160235788747929189818670114307838629323071300103922811544q^{68} \) \(\mathstrut +\mathstrut 515562382253181099403631333636444425682719138024450821171960q^{69} \) \(\mathstrut -\mathstrut 353452742508352350629180180209243686856254792372732375699360q^{70} \) \(\mathstrut +\mathstrut 2545358340513829895032036249420402481032689044213009966226072q^{71} \) \(\mathstrut +\mathstrut 1858945486865276880358111291017384807342443001621072587876040q^{72} \) \(\mathstrut +\mathstrut 3634977497989942338742619849045326181579380691267081786286574q^{73} \) \(\mathstrut +\mathstrut 149583309261260981035291220208421583145787523307449684577780q^{74} \) \(\mathstrut +\mathstrut 10696723504727567017466932174990112704208756054655428010059199q^{75} \) \(\mathstrut +\mathstrut 44361120066033071202297700264247326844962699790882280597066256q^{76} \) \(\mathstrut +\mathstrut 2787248977771439879133771326299195120236233874908828948231616q^{77} \) \(\mathstrut -\mathstrut 106265191857555529652912639480974518139485750547126143003068268q^{78} \) \(\mathstrut -\mathstrut 108655335736204494196797419786154330065071415921774578973266280q^{79} \) \(\mathstrut +\mathstrut 179560660082718156951752908874134790268568122556519286027263584q^{80} \) \(\mathstrut +\mathstrut 129692030355124414886729601475537705322460327515034252200066571q^{81} \) \(\mathstrut -\mathstrut 168419268813352074152696966965808331803790274705328080277502804q^{82} \) \(\mathstrut +\mathstrut 666627046677300801346778718286597552251089160284541426205968804q^{83} \) \(\mathstrut -\mathstrut 331674076073398934614361651600449683185481641659738305163284960q^{84} \) \(\mathstrut +\mathstrut 786799842934726755368361154177969111250132467557215049805840692q^{85} \) \(\mathstrut +\mathstrut 3968876794345165854405432735391216331676546435218946806435253576q^{86} \) \(\mathstrut -\mathstrut 867601494999151460698344619816437149071908525696131488359152970q^{87} \) \(\mathstrut -\mathstrut 2077235424923546695469227475479972617537370996634929957934965920q^{88} \) \(\mathstrut -\mathstrut 4536175169951302186672349499218286573665856269622401182182043266q^{89} \) \(\mathstrut +\mathstrut 2126957600986948340851269773340826280278381785499943528917334484q^{90} \) \(\mathstrut -\mathstrut 314695945056081124071893638454701863459317027331441499799145760q^{91} \) \(\mathstrut -\mathstrut 19275072315136785302212715588188105426215864541962442912799580192q^{92} \) \(\mathstrut -\mathstrut 1775852494856519753498069159890217952992787969833659295644550088q^{93} \) \(\mathstrut +\mathstrut 50765461892948731039539028852525696414382626889183735875700898912q^{94} \) \(\mathstrut +\mathstrut 44116504798438205038497735588871663814704993634734088042403260664q^{95} \) \(\mathstrut +\mathstrut 105274360098785049511479634643100239619245690316279881631113940000q^{96} \) \(\mathstrut +\mathstrut 161640138220417791770996425132391296550980884122633329592007400918q^{97} \) \(\mathstrut -\mathstrut 172788674287647322793549412320988559853203256576665666003433893074q^{98} \) \(\mathstrut +\mathstrut 352913032246277614719360267290575261406563762380876948694185756q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{66}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.66.a.a \(5\) \(80.272\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-2586530964\) \(-9\!\cdots\!05\) \(-8\!\cdots\!94\) \(57\!\cdots\!24\) \(+\) \(q+(-517306193-\beta _{1})q^{2}-3^{32}q^{3}+\cdots\)
3.66.a.b \(6\) \(80.272\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6210982962\) \(11\!\cdots\!46\) \(35\!\cdots\!00\) \(13\!\cdots\!04\) \(-\) \(q+(1035163827+\beta _{1})q^{2}+3^{32}q^{3}+\cdots\)

Decomposition of \(S_{66}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{66}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{66}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)