Properties

Label 8.7
Level 8
Weight 7
Dimension 5
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 28
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(8))\).

Total New Old
Modular forms 15 7 8
Cusp forms 9 5 4
Eisenstein series 6 2 4

Trace form

\( 5 q - 6 q^{2} - 2 q^{3} + 20 q^{4} + 28 q^{6} - 264 q^{8} + 727 q^{9} + O(q^{10}) \) \( 5 q - 6 q^{2} - 2 q^{3} + 20 q^{4} + 28 q^{6} - 264 q^{8} + 727 q^{9} - 1920 q^{10} - 1362 q^{11} + 4312 q^{12} + 5760 q^{14} - 10480 q^{16} + 2442 q^{17} - 21506 q^{18} - 3938 q^{19} + 31680 q^{20} + 43132 q^{22} - 61808 q^{24} - 8275 q^{25} - 59520 q^{26} + 32860 q^{27} + 59520 q^{28} + 90240 q^{30} - 81696 q^{32} - 23500 q^{33} - 68108 q^{34} - 49920 q^{35} + 75868 q^{36} + 46428 q^{38} - 13440 q^{40} + 16698 q^{41} + 38400 q^{42} + 122542 q^{43} - 112488 q^{44} - 213120 q^{46} + 326368 q^{48} + 119765 q^{49} + 232650 q^{50} - 465412 q^{51} - 254400 q^{52} - 495368 q^{54} + 349440 q^{56} + 12500 q^{57} + 516480 q^{58} + 846990 q^{59} - 716160 q^{60} - 407040 q^{62} + 726080 q^{64} - 205440 q^{65} + 717608 q^{66} - 1386818 q^{67} - 324312 q^{68} - 360960 q^{70} + 95656 q^{72} - 149222 q^{73} - 32640 q^{74} + 2483950 q^{75} - 88232 q^{76} + 324480 q^{78} - 1032960 q^{80} - 186839 q^{81} - 672428 q^{82} - 2786082 q^{83} + 602880 q^{84} + 1588860 q^{86} - 753392 q^{88} + 403962 q^{89} - 1296000 q^{90} + 3398400 q^{91} + 2743680 q^{92} + 971520 q^{94} - 1760192 q^{96} + 895978 q^{97} - 3332454 q^{98} - 5702086 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.7.c \(\chi_{8}(7, \cdot)\) None 0 1
8.7.d \(\chi_{8}(3, \cdot)\) 8.7.d.a 1 1
8.7.d.b 4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)