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Properties

Label 8.11
Level 8
Weight 11
Dimension 9
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 44
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(44\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(8))\).

Total New Old
Modular forms 23 11 12
Cusp forms 17 9 8
Eisenstein series 6 2 4

Trace form

\( 9 q + 10 q^{2} - 2 q^{3} + 1236 q^{4} + 10012 q^{6} - 32840 q^{8} + 137779 q^{9} + O(q^{10}) \) \( 9 q + 10 q^{2} - 2 q^{3} + 1236 q^{4} + 10012 q^{6} - 32840 q^{8} + 137779 q^{9} + 9120 q^{10} + 45902 q^{11} - 313448 q^{12} - 400320 q^{14} - 938736 q^{16} + 452882 q^{17} - 2477042 q^{18} + 5107038 q^{19} + 2557440 q^{20} + 4666812 q^{22} - 4000112 q^{24} - 9027135 q^{25} + 1891680 q^{26} - 26107748 q^{27} + 18286080 q^{28} + 67026240 q^{30} - 97571360 q^{32} - 27349372 q^{33} - 142063212 q^{34} + 53736960 q^{35} + 228065116 q^{36} + 267808988 q^{38} - 357584640 q^{40} + 54890402 q^{41} - 576155520 q^{42} + 204294990 q^{43} + 628067288 q^{44} + 851947200 q^{46} - 1648174112 q^{48} + 202043001 q^{49} - 1981861190 q^{50} - 673729540 q^{51} + 2420759040 q^{52} + 3511590520 q^{54} - 2928529920 q^{56} - 215783068 q^{57} - 3245264160 q^{58} - 44598418 q^{59} + 5250055680 q^{60} + 4060980480 q^{62} - 4730963904 q^{64} - 839028480 q^{65} - 7472960920 q^{66} + 588125502 q^{67} + 6101561768 q^{68} + 7723829760 q^{70} - 10021483928 q^{72} + 1194291138 q^{73} - 7669373280 q^{74} - 221476850 q^{75} + 7187666712 q^{76} + 7176312000 q^{78} - 6408629760 q^{80} + 4396660573 q^{81} - 2429852748 q^{82} + 1949474078 q^{83} - 2916218880 q^{84} - 3841359172 q^{86} + 9008033808 q^{88} - 4953423262 q^{89} + 12545940960 q^{90} + 7645985280 q^{91} - 8903892480 q^{92} - 14182177920 q^{94} + 24050761792 q^{96} - 19570841550 q^{97} + 25720660330 q^{98} - 30528237382 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.11.c \(\chi_{8}(7, \cdot)\) None 0 1
8.11.d \(\chi_{8}(3, \cdot)\) 8.11.d.a 1 1
8.11.d.b 8

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)