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Properties

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

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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