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Properties

Label 8.6
Level 8
Weight 6
Dimension 5
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(8))\).

Total New Old
Modular forms 13 7 6
Cusp forms 7 5 2
Eisenstein series 6 2 4

Trace form

\( 5 q - 2 q^{2} + 20 q^{3} + 20 q^{4} - 74 q^{5} - 116 q^{6} + 72 q^{7} - 248 q^{8} - 7 q^{9} + O(q^{10}) \) \( 5 q - 2 q^{2} + 20 q^{3} + 20 q^{4} - 74 q^{5} - 116 q^{6} + 72 q^{7} - 248 q^{8} - 7 q^{9} + 632 q^{10} + 124 q^{11} + 1576 q^{12} + 478 q^{13} - 2384 q^{14} - 1896 q^{15} - 3312 q^{16} - 998 q^{17} + 4754 q^{18} + 3044 q^{19} + 4624 q^{20} - 480 q^{21} - 5636 q^{22} + 2520 q^{23} - 7792 q^{24} + 3907 q^{25} + 5608 q^{26} - 1720 q^{27} + 5152 q^{28} - 3282 q^{29} - 2128 q^{30} - 18656 q^{31} + 5408 q^{32} + 128 q^{33} - 4772 q^{34} + 1776 q^{35} - 10164 q^{36} + 10326 q^{37} + 15980 q^{38} + 44664 q^{39} + 16032 q^{40} - 13454 q^{41} - 26144 q^{42} - 9188 q^{43} - 29112 q^{44} - 11618 q^{45} + 29200 q^{46} - 31056 q^{47} + 35616 q^{48} - 6403 q^{49} - 47498 q^{50} - 23960 q^{51} - 36560 q^{52} + 11686 q^{53} + 23288 q^{54} + 76296 q^{55} + 40768 q^{56} + 58848 q^{57} + 3784 q^{58} + 16876 q^{59} + 2592 q^{60} - 18482 q^{61} + 34496 q^{62} - 157208 q^{63} - 41920 q^{64} - 54892 q^{65} + 43224 q^{66} - 15532 q^{67} + 10344 q^{68} + 3680 q^{69} - 68928 q^{70} + 174728 q^{71} - 83272 q^{72} + 35090 q^{73} + 17464 q^{74} + 47020 q^{75} + 99944 q^{76} - 2976 q^{77} - 174064 q^{78} - 203312 q^{79} - 35520 q^{80} - 42867 q^{81} + 161132 q^{82} + 67364 q^{83} + 196672 q^{84} + 88652 q^{85} - 18500 q^{86} + 242232 q^{87} - 167216 q^{88} - 12638 q^{89} + 142280 q^{90} - 11472 q^{91} - 49056 q^{92} - 114560 q^{93} - 98784 q^{94} - 485000 q^{95} - 115648 q^{96} - 50710 q^{97} - 117042 q^{98} + 19468 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.6.a \(\chi_{8}(1, \cdot)\) 8.6.a.a 1 1
8.6.b \(\chi_{8}(5, \cdot)\) 8.6.b.a 4 1

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)