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Properties

Label 17.5
Level 17
Weight 5
Dimension 40
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 120
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(17))\).

Total New Old
Modular forms 56 56 0
Cusp forms 40 40 0
Eisenstein series 16 16 0

Trace form

\( 40 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 40 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + 376 q^{10} + 112 q^{11} - 776 q^{12} - 416 q^{13} - 776 q^{14} - 704 q^{15} + 256 q^{17} + 2032 q^{18} + 688 q^{19} + 2680 q^{20} + 2032 q^{21} + 760 q^{22} - 176 q^{23} + 1672 q^{24} - 2600 q^{26} - 2600 q^{27} - 7448 q^{28} - 3368 q^{29} - 9800 q^{30} - 3720 q^{31} - 2400 q^{32} + 4280 q^{34} + 4208 q^{35} + 11960 q^{36} + 7416 q^{37} + 16720 q^{38} + 15624 q^{39} + 20280 q^{40} + 2656 q^{41} - 6392 q^{42} - 7512 q^{43} - 31592 q^{44} - 23368 q^{45} - 25752 q^{46} - 10208 q^{47} - 14080 q^{48} - 3112 q^{49} + 3224 q^{51} + 12784 q^{52} + 24424 q^{53} + 51672 q^{54} + 26648 q^{55} + 40432 q^{56} + 10352 q^{57} - 4336 q^{58} - 3176 q^{59} - 38896 q^{60} - 24600 q^{61} - 39248 q^{62} - 55664 q^{63} - 45560 q^{64} - 37928 q^{65} - 29376 q^{66} + 34912 q^{68} + 46592 q^{69} + 59536 q^{70} + 21736 q^{71} + 59824 q^{72} + 28592 q^{73} + 15976 q^{74} + 46168 q^{75} - 9280 q^{76} + 2392 q^{77} - 6048 q^{78} - 15912 q^{79} - 47640 q^{80} - 48696 q^{81} - 58368 q^{82} - 27296 q^{83} + 18872 q^{85} + 74336 q^{86} + 38536 q^{87} + 55608 q^{88} - 1232 q^{89} - 24136 q^{90} - 7800 q^{91} - 27032 q^{92} - 32232 q^{93} - 37096 q^{94} - 49640 q^{95} - 79696 q^{96} - 12392 q^{97} - 76304 q^{98} + 6056 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.5.e \(\chi_{17}(3, \cdot)\) 17.5.e.a 40 8