## Defining parameters

 Level: $$N$$ = $$17$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$1$$ Newforms: $$2$$ Sturm bound: $$72$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(17))$$.

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

## Trace form

 $$16q - 8q^{2} - 8q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 8q^{9} + O(q^{10})$$ $$16q - 8q^{2} - 8q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 8q^{9} + 16q^{10} + 32q^{11} + 88q^{12} + 16q^{13} + 24q^{14} + 16q^{15} - 16q^{17} - 80q^{18} - 32q^{19} - 120q^{20} - 128q^{21} - 104q^{22} - 64q^{23} - 56q^{24} + 80q^{25} + 176q^{26} + 136q^{27} + 232q^{28} + 72q^{29} + 184q^{30} + 56q^{31} + 64q^{32} - 72q^{34} - 80q^{35} - 232q^{36} - 136q^{37} - 112q^{38} - 24q^{39} - 136q^{40} + 48q^{41} - 56q^{42} - 136q^{43} + 24q^{44} - 88q^{45} - 88q^{46} + 112q^{47} + 224q^{48} + 24q^{49} - 40q^{51} - 144q^{52} + 64q^{53} + 216q^{54} + 216q^{55} - 48q^{56} + 272q^{57} + 240q^{58} - 40q^{59} + 80q^{60} + 104q^{61} - 304q^{62} + 64q^{63} - 184q^{64} - 128q^{65} + 96q^{68} + 32q^{69} + 144q^{70} + 72q^{71} + 64q^{72} + 72q^{73} + 16q^{74} - 488q^{75} - 264q^{77} - 768q^{78} - 232q^{79} - 216q^{80} - 648q^{81} - 472q^{82} - 352q^{83} + 240q^{85} + 1120q^{86} + 520q^{87} + 440q^{88} + 448q^{89} + 704q^{90} + 296q^{91} + 360q^{92} + 216q^{93} + 24q^{94} + 120q^{95} + 272q^{96} - 296q^{97} - 104q^{98} - 88q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(17))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
17.3.e $$\chi_{17}(3, \cdot)$$ 17.3.e.a 8 8
17.3.e.b 8