Properties

Label 3.38
Level 3
Weight 38
Dimension 7
Nonzero newspaces 1
Newforms 2
Sturm bound 25
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 38 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(25\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_1(3))\).

Total New Old
Modular forms 13 7 6
Cusp forms 11 7 4
Eisenstein series 2 0 2

Trace form

\( 7q + 126654q^{2} + 387420489q^{3} + 684575556340q^{4} - 13728547643694q^{5} + 289972613401830q^{6} + 1983925604451440q^{7} + 47100204248248488q^{8} + 1050662447078993847q^{9} + O(q^{10}) \) \( 7q + 126654q^{2} + 387420489q^{3} + 684575556340q^{4} - 13728547643694q^{5} + 289972613401830q^{6} + 1983925604451440q^{7} + 47100204248248488q^{8} + 1050662447078993847q^{9} + 10677439113740148564q^{10} + 43627012209334921596q^{11} + 2953056363509900916q^{12} - 116439107414805217342q^{13} - 1011900338090011919184q^{14} + 2142004542906729634254q^{15} + 87255901380513400366096q^{16} + 53933221344537261354222q^{17} + 19010085938906126671134q^{18} + 37431357216330735837572q^{19} - 7632340044421182766445256q^{20} + 4349838812892944922819792q^{21} + 19422800609832966452458824q^{22} - 23262632371810686242267160q^{23} + 90605263613645777821825896q^{24} + 70500389161904121000790441q^{25} - 190049008972894374663386556q^{26} + 58149737003040059690390169q^{27} + 436404251980738279231633760q^{28} + 4282387159715215775639357514q^{29} - 4153326304813313427219998844q^{30} - 2864027368599097964995766872q^{31} + 9236041216446580613557668000q^{32} - 666206143987247432978609916q^{33} + 12435643218207912669769044060q^{34} + 89869427129508625745958757920q^{35} + 102751118462092574391065977140q^{36} + 115863671844314605837317826490q^{37} - 1107633303229040631381110062344q^{38} + 85271595592601424874818976542q^{39} - 930670397641098462628460596752q^{40} + 1217769522923831842591596907158q^{41} - 1009658064856086695606942529360q^{42} + 1974001937268466063840199045564q^{43} + 7123114228038704575669086836208q^{44} - 2060581351737727564473739192974q^{45} - 19159636947469943799013210624752q^{46} - 7493630272642461617006238652512q^{47} + 8954664258664264102770633426576q^{48} + 17777681797108039345187920072047q^{49} + 6073272961727520596403935775714q^{50} + 41946140543332132836242206168626q^{51} + 229991532199618315922613932880152q^{52} - 241155436559598971130695435510670q^{53} + 43523333654665393476466329791430q^{54} - 453860871097216155007773977194104q^{55} + 679813569394113295052284624175040q^{56} - 436483358600513385501061741356804q^{57} - 177250208537205591084553136157468q^{58} - 231030154028789531327080142644452q^{59} + 193777584194928096043010367942456q^{60} - 915631926311408975897805450272158q^{61} - 3526030476634524366768610629595200q^{62} + 297776590056517422675871367184240q^{63} + 7489482758536410774431040832535104q^{64} - 5918935767911995666073259191789892q^{65} + 11001043672663058443826467735295592q^{66} + 20037212315258745158622400365789092q^{67} - 14964628486001657391340224710150232q^{68} + 4281679486048626419130782999386776q^{69} - 34853363080158496834151256770488800q^{70} - 11256928646966945694391516939711656q^{71} + 7069487979055025456312146725579048q^{72} + 13286862853326838922960192885928230q^{73} - 42636436263036741069505645420848684q^{74} + 46604114812831642145212466210638599q^{75} + 251585815873023986043650792581090448q^{76} - 317311456849407219291248056732618560q^{77} + 405690213954176805237105803184658548q^{78} + 117214277910546077013071739760375160q^{79} - 1573122528355469898112660077331279776q^{80} + 157698796814574220882881035123408487q^{81} + 439407919632883552581457950171236460q^{82} - 780620880363296415782883626608968828q^{83} + 1744656585209134598679469690579281504q^{84} + 2058649870565625761770386988960299492q^{85} - 3018614020714216403538494878879907064q^{86} + 1572921319640150885314260279379461462q^{87} + 2856972222974864440117459932508175328q^{88} - 1919002589120493935902265256833893578q^{89} + 1602626329682741114871197285917412244q^{90} + 3074815552050522621982938457870992928q^{91} - 22025423841918805162477656924353262240q^{92} + 8079908710240208253230295102126005400q^{93} + 14581692702710050867156722254196766752q^{94} - 19671761716261279025385552016851096456q^{95} + 24717005554576238245245842290026843552q^{96} + 3135834703288340273897746546516640462q^{97} - 44762639877851592030494418305208632178q^{98} + 6548180486657852927733977168615917116q^{99} + O(q^{100}) \)

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.38.a \(\chi_{3}(1, \cdot)\) 3.38.a.a 3 1
3.38.a.b 4

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)