Properties

Label 8.12
Level 8
Weight 12
Dimension 13
Nonzero newspaces 2
Newforms 3
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(8))\).

Total New Old
Modular forms 25 15 10
Cusp forms 19 13 6
Eisenstein series 6 2 4

Trace form

\( 13q + 22q^{2} + 20q^{3} + 436q^{4} + 4378q^{5} - 24308q^{6} + 1976q^{7} - 208472q^{8} - 108043q^{9} + O(q^{10}) \) \( 13q + 22q^{2} + 20q^{3} + 436q^{4} + 4378q^{5} - 24308q^{6} + 1976q^{7} - 208472q^{8} - 108043q^{9} + 29864q^{10} - 437924q^{11} - 476216q^{12} + 2424354q^{13} + 2264272q^{14} - 6977400q^{15} + 3757072q^{16} + 14211466q^{17} + 2329130q^{18} - 29163996q^{19} + 8296432q^{20} + 42049248q^{21} - 24201892q^{22} - 41608536q^{23} + 10668944q^{24} - 16272585q^{25} - 101931080q^{26} + 67917320q^{27} - 95722144q^{28} - 242433102q^{29} + 261362768q^{30} + 739918304q^{31} + 343908512q^{32} - 647584936q^{33} - 187103796q^{34} + 101747952q^{35} - 431195700q^{36} - 182227398q^{37} + 375100844q^{38} + 394990152q^{39} + 1519138784q^{40} + 324867634q^{41} - 3697737056q^{42} - 1743278724q^{43} - 4127012952q^{44} + 2138827042q^{45} + 6028867440q^{46} - 1261796400q^{47} + 9357606048q^{48} + 4008659349q^{49} - 9626584226q^{50} - 9990058520q^{51} - 11595427248q^{52} - 531170102q^{53} + 20050494008q^{54} + 15767737912q^{55} + 18698733760q^{56} - 5229281640q^{57} - 22828679464q^{58} - 9014835572q^{59} - 43681325472q^{60} - 1840230702q^{61} + 40774631744q^{62} + 21964258552q^{63} + 55266728512q^{64} - 10900501924q^{65} - 83128448712q^{66} - 2485905324q^{67} - 83303223768q^{68} - 19932595552q^{69} + 100120831168q^{70} + 18720070520q^{71} + 112862051672q^{72} + 36321508754q^{73} - 102103996184q^{74} - 81254774516q^{75} - 97501928568q^{76} + 14365261728q^{77} + 144445560944q^{78} + 105049383344q^{79} + 128322038976q^{80} - 2226964707q^{81} - 123309929604q^{82} - 147967912348q^{83} - 199990865984q^{84} + 86218163220q^{85} + 130201908124q^{86} - 26582565432q^{87} + 169216119632q^{88} - 26522388350q^{89} - 228506434984q^{90} + 7178123184q^{91} - 141139403232q^{92} - 32147884160q^{93} + 145336130016q^{94} + 58741871848q^{95} + 109508068928q^{96} - 10556170438q^{97} - 6194726778q^{98} + 113298667660q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.12.a \(\chi_{8}(1, \cdot)\) 8.12.a.a 1 1
8.12.a.b 2
8.12.b \(\chi_{8}(5, \cdot)\) 8.12.b.a 10 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)