Properties

Label 8.5
Level 8
Weight 5
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 20
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(8))\).

Total New Old
Modular forms 11 5 6
Cusp forms 5 3 2
Eisenstein series 6 2 4

Trace form

\( 3 q + 2 q^{2} - 2 q^{3} - 12 q^{4} - 68 q^{6} + 152 q^{8} + 25 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{2} - 2 q^{3} - 12 q^{4} - 68 q^{6} + 152 q^{8} + 25 q^{9} + 240 q^{10} - 98 q^{11} - 392 q^{12} - 480 q^{14} + 528 q^{16} - 122 q^{17} + 550 q^{18} + 702 q^{19} - 480 q^{20} - 132 q^{22} - 368 q^{24} - 45 q^{25} - 240 q^{26} - 1988 q^{27} + 960 q^{28} + 1440 q^{30} - 928 q^{32} + 332 q^{33} - 2748 q^{34} + 3840 q^{35} + 3100 q^{36} + 1468 q^{38} - 2880 q^{40} + 742 q^{41} - 2880 q^{42} - 7266 q^{43} - 8 q^{44} + 2400 q^{46} - 1952 q^{48} - 477 q^{49} + 3170 q^{50} + 10748 q^{51} + 480 q^{52} - 392 q^{54} + 5760 q^{56} - 4468 q^{57} + 2640 q^{58} - 10274 q^{59} - 2880 q^{60} - 9600 q^{62} + 3648 q^{64} + 1920 q^{65} + 2888 q^{66} + 10878 q^{67} - 15512 q^{68} - 3840 q^{70} + 3400 q^{72} + 10278 q^{73} + 13680 q^{74} - 12770 q^{75} + 3192 q^{76} - 1440 q^{78} + 13440 q^{80} - 4433 q^{81} - 6972 q^{82} + 6718 q^{83} + 5760 q^{84} - 10244 q^{86} - 5232 q^{88} - 14618 q^{89} - 10800 q^{90} - 3840 q^{91} - 4800 q^{92} + 16320 q^{94} - 26048 q^{96} + 7494 q^{97} + 12482 q^{98} - 2950 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8.5.c \(\chi_{8}(7, \cdot)\) None 0 1
8.5.d \(\chi_{8}(3, \cdot)\) 8.5.d.a 1 1
8.5.d.b 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)