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Properties

Label 17.7
Level 17
Weight 7
Dimension 64
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 168
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(17))\).

Total New Old
Modular forms 80 80 0
Cusp forms 64 64 0
Eisenstein series 16 16 0

Trace form

\( 64 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 64 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + 3736 q^{10} - 4488 q^{11} - 7688 q^{12} + 2872 q^{13} + 12152 q^{14} + 14776 q^{15} - 6408 q^{17} - 44816 q^{18} - 11528 q^{19} - 19720 q^{20} + 18232 q^{21} + 40312 q^{22} + 29112 q^{23} + 135304 q^{24} - 92840 q^{25} - 214536 q^{26} - 58328 q^{27} + 42472 q^{28} + 73832 q^{29} + 326584 q^{30} + 153784 q^{31} + 118304 q^{32} - 213320 q^{34} - 200400 q^{35} - 513736 q^{36} - 255368 q^{37} + 73872 q^{38} + 11064 q^{39} - 97736 q^{40} - 145768 q^{41} + 234376 q^{42} + 342952 q^{43} + 593048 q^{44} + 138152 q^{45} - 324632 q^{46} + 601912 q^{47} + 991424 q^{48} + 224248 q^{49} - 243208 q^{51} - 933904 q^{52} + 255280 q^{53} - 829992 q^{54} - 1389704 q^{55} - 2611408 q^{56} - 1982968 q^{57} - 909104 q^{58} + 463608 q^{59} + 3097040 q^{60} + 1713112 q^{61} + 3651696 q^{62} + 3783736 q^{63} + 1245576 q^{64} + 246112 q^{65} - 78336 q^{66} + 680096 q^{68} - 1859536 q^{69} - 4027696 q^{70} - 2283784 q^{71} - 8433296 q^{72} - 4507328 q^{73} - 2595128 q^{74} - 1608968 q^{75} + 1378048 q^{76} + 2587736 q^{77} + 8752032 q^{78} + 4152952 q^{79} + 9312744 q^{80} + 6663624 q^{81} + 4368928 q^{82} + 2470824 q^{83} - 4498640 q^{85} - 6837408 q^{86} - 7591592 q^{87} - 13258952 q^{88} - 5755208 q^{89} - 11377576 q^{90} - 4157576 q^{91} - 1636888 q^{92} + 2508024 q^{93} + 7744792 q^{94} + 8552600 q^{95} + 19873136 q^{96} + 6505336 q^{97} + 15189328 q^{98} + 14554736 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.7.e \(\chi_{17}(3, \cdot)\) 17.7.e.a 64 8