Properties

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

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
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

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

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 the 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

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