## Defining parameters

 Level: $$N$$ = $$17$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newforms: $$5$$ Sturm bound: $$96$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(17))$$.

Total New Old
Modular forms 44 42 2
Cusp forms 28 28 0
Eisenstein series 16 14 2

## Trace form

 $$28q - 8q^{2} - 8q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 8q^{9} + O(q^{10})$$ $$28q - 8q^{2} - 8q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 8q^{9} - 112q^{10} - 120q^{11} - 104q^{12} + 24q^{13} + 152q^{14} + 328q^{15} + 432q^{16} + 120q^{17} + 432q^{18} + 72q^{19} + 104q^{20} - 104q^{21} - 232q^{22} - 216q^{23} - 1880q^{24} - 1236q^{25} - 1040q^{26} - 224q^{27} + 136q^{28} + 252q^{29} + 1336q^{30} + 856q^{31} + 1168q^{32} + 1040q^{33} + 2104q^{34} + 976q^{35} + 1656q^{36} + 664q^{37} - 336q^{38} - 1224q^{39} - 2504q^{40} - 1428q^{41} - 2936q^{42} - 1472q^{43} - 1960q^{44} - 1348q^{45} - 1016q^{46} + 1512q^{47} + 3296q^{48} + 1528q^{49} + 2784q^{50} + 1592q^{51} + 3056q^{52} - 316q^{53} - 2696q^{54} - 1896q^{55} - 1008q^{56} - 2096q^{57} - 1488q^{58} - 872q^{59} - 1424q^{60} + 232q^{61} - 1872q^{62} + 1960q^{63} - 2104q^{64} + 1092q^{65} + 5168q^{66} + 2128q^{67} + 3632q^{68} + 3728q^{69} + 1264q^{70} + 184q^{71} + 48q^{72} + 292q^{73} + 256q^{74} + 856q^{75} + 480q^{76} - 216q^{77} - 1792q^{78} - 360q^{79} - 872q^{80} - 2992q^{81} - 424q^{82} - 5504q^{83} - 8352q^{84} - 4316q^{85} - 8512q^{86} - 1496q^{87} + 1720q^{88} - 1112q^{89} - 1056q^{90} + 1432q^{91} + 3464q^{92} + 2232q^{93} + 3928q^{94} + 3880q^{95} + 5984q^{96} + 280q^{97} + 8568q^{98} - 2616q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(17))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
17.4.a $$\chi_{17}(1, \cdot)$$ 17.4.a.a 1 1
17.4.a.b 3
17.4.b $$\chi_{17}(16, \cdot)$$ 17.4.b.a 4 1
17.4.c $$\chi_{17}(4, \cdot)$$ 17.4.c.a 8 2
17.4.d $$\chi_{17}(2, \cdot)$$ 17.4.d.a 12 4