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Properties

Label 3.37
Level 3
Weight 37
Dimension 11
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 37 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(\Gamma_1(3))\).

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

Trace form

\( 11 q - 164736261 q^{3} - 366480813328 q^{4} + 77238909590832 q^{6} + 1529656139588998 q^{7} + 219422675471657499 q^{9} + O(q^{10}) \) \( 11 q - 164736261 q^{3} - 366480813328 q^{4} + 77238909590832 q^{6} + 1529656139588998 q^{7} + 219422675471657499 q^{9} + 976353968400999840 q^{10} + 12713663984972326704 q^{12} - 26664183895525067642 q^{13} + 7346306914204243680 q^{15} + 12912742276961748775040 q^{16} - 116380061882656121268000 q^{18} + 138821577295896839366518 q^{19} - 2247956081834234679653850 q^{21} + 6375713195756021276887200 q^{22} - 18479722715707703137259904 q^{24} + 7279508127194401821131675 q^{25} + 95231216966669978862527019 q^{27} - 391577988767589793638714272 q^{28} + 832077359475776822335514400 q^{30} - 1733608557857573255379602138 q^{31} - 1833168501223628340439879200 q^{33} + 11044532239488942328340194176 q^{34} - 21948402658393775440817520912 q^{36} + 12786450877411433164392216358 q^{37} - 9936827303902532409454966170 q^{39} + 14850499435375431475622142720 q^{40} + 551003488989169331884355647200 q^{42} - 515487319179727929010406869802 q^{43} - 75992211973807694886478996800 q^{45} - 887182867438274648036289139776 q^{46} - 4346257047411219928317289501056 q^{48} + 9110404204240350847814031518529 q^{49} - 2349347159740543712848217109888 q^{51} - 13203626071464804773830678836512 q^{52} + 35390782846752825865826083751568 q^{54} - 30568574550133842572339360395200 q^{55} + 96963716675033228271210975522198 q^{57} - 112605799975805654976196455444000 q^{58} + 19469866547367779716225803605760 q^{60} + 66999347224237022458014520403782 q^{61} - 20218845986102637586445162314842 q^{63} - 304236018528391125615295992251392 q^{64} + 1808913396822349027193824888380960 q^{66} - 3004194906649294236056896403510282 q^{67} + 5226032060124551681525948207907648 q^{69} - 11529100185846942980259125797809600 q^{70} + 19879821238248816464160255047788800 q^{72} - 10390545366461872145216469125969162 q^{73} + 21376990929305061495027761443252875 q^{75} - 39862084315848733842646101136440224 q^{76} + 66756441224105756984056960627624800 q^{78} - 71385979381146382550075928433902362 q^{79} + 124901631937240804827635146103482731 q^{81} - 295731520386077266321378186874491200 q^{82} + 565465498335095720662452392509252320 q^{84} - 416995278796335191384264774379644160 q^{85} + 502161755301600073278417594406864800 q^{87} - 1043368725545479380062123692743456000 q^{88} + 1148239664725140620121403824942828960 q^{90} - 676075249402808126607982688855079700 q^{91} + 1136822552118204808049516782296691398 q^{93} - 1775468098694354855547362712124166784 q^{94} + 2402404280227868861578148783194622976 q^{96} - 1638469121614694224091416117067972522 q^{97} + 2995711137935834844910948248309577920 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{37}^{\mathrm{new}}(\Gamma_1(3))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.37.b \(\chi_{3}(2, \cdot)\) 3.37.b.a 1 1
3.37.b.b 10