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Properties

Label 17.8
Level 17
Weight 8
Dimension 76
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 192
Trace bound 2

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(17))\).

Total New Old
Modular forms 92 90 2
Cusp forms 76 76 0
Eisenstein series 16 14 2

Trace form

\( 76 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 76 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 9832 q^{10} + 15440 q^{11} - 19976 q^{12} - 19152 q^{13} - 14472 q^{14} + 50368 q^{15} + 114672 q^{16} + 26096 q^{17} - 18192 q^{18} - 45360 q^{19} - 249096 q^{20} - 165344 q^{21} + 32120 q^{22} + 120848 q^{23} + 364648 q^{24} + 514084 q^{25} + 73912 q^{26} - 227456 q^{27} - 1141112 q^{28} - 466468 q^{29} - 651464 q^{30} + 292568 q^{31} + 1070288 q^{32} + 1149968 q^{33} + 2082360 q^{34} + 518736 q^{35} - 607560 q^{36} - 1200232 q^{37} - 4255232 q^{38} - 1404792 q^{39} + 521656 q^{40} + 1591508 q^{41} + 2778280 q^{42} + 1834032 q^{43} - 1918376 q^{44} - 2381188 q^{45} - 6529592 q^{46} + 113712 q^{47} + 4708256 q^{48} + 3311576 q^{49} + 6999984 q^{50} + 3753560 q^{51} + 5107696 q^{52} - 5471980 q^{53} + 177448 q^{54} + 4418104 q^{55} - 5770928 q^{56} - 3330680 q^{57} - 9309392 q^{58} - 8559432 q^{59} - 21349904 q^{60} - 7438632 q^{61} + 8277584 q^{62} + 4263712 q^{63} + 9726792 q^{64} + 4835652 q^{65} + 14785376 q^{66} + 9624400 q^{67} + 9862272 q^{68} + 20709824 q^{69} + 25222064 q^{70} + 7683208 q^{71} + 1986192 q^{72} - 16437108 q^{73} - 27325496 q^{74} - 56823944 q^{75} - 53778592 q^{76} - 27397048 q^{77} - 24788032 q^{78} + 2998072 q^{79} + 33766808 q^{80} + 57343040 q^{81} + 60544896 q^{82} - 263880 q^{83} + 807648 q^{84} + 12420644 q^{85} + 97258240 q^{86} + 58707160 q^{87} + 40894392 q^{88} - 363824 q^{89} - 73706136 q^{90} - 76461240 q^{91} - 162955832 q^{92} - 84107496 q^{93} - 121957416 q^{94} - 58226040 q^{95} - 41737312 q^{96} + 16854264 q^{97} + 96651936 q^{98} + 65051040 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.8.a \(\chi_{17}(1, \cdot)\) 17.8.a.a 1 1
17.8.a.b 3
17.8.a.c 6
17.8.b \(\chi_{17}(16, \cdot)\) 17.8.b.a 10 1
17.8.c \(\chi_{17}(4, \cdot)\) 17.8.c.a 20 2
17.8.d \(\chi_{17}(2, \cdot)\) 17.8.d.a 36 4