## Defining parameters

 Level: $$N$$ = $$17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(17))$$.

Total New Old
Modular forms 20 20 0
Cusp forms 5 5 0
Eisenstein series 15 15 0

## Trace form

 $$5q - 5q^{2} - 4q^{3} - q^{4} - 2q^{5} + 4q^{6} + 7q^{8} + 5q^{9} + O(q^{10})$$ $$5q - 5q^{2} - 4q^{3} - q^{4} - 2q^{5} + 4q^{6} + 7q^{8} + 5q^{9} + 6q^{10} - 4q^{11} - 4q^{12} - 2q^{13} - 8q^{15} - 13q^{16} + q^{17} - 9q^{18} + 4q^{19} + 6q^{20} + 12q^{22} + 8q^{23} + 12q^{24} - 5q^{25} - 2q^{26} + 8q^{27} + 2q^{29} - 8q^{31} - q^{32} - 21q^{34} + 3q^{36} - 2q^{37} + 4q^{38} - 14q^{40} - 10q^{41} - 8q^{42} - 4q^{43} - 20q^{44} + 18q^{45} + 16q^{46} + 12q^{48} + 17q^{49} + 21q^{50} + 28q^{51} + 18q^{52} + 2q^{53} - 8q^{54} - 8q^{56} - 24q^{57} - 6q^{58} - 12q^{59} - 8q^{60} - 10q^{61} - 16q^{62} - 24q^{63} + 7q^{64} + 8q^{66} + 20q^{67} + 11q^{68} - 32q^{69} + 16q^{71} - 9q^{72} - 34q^{73} + 22q^{74} - 12q^{75} + 12q^{76} + 8q^{77} - 8q^{78} + 8q^{79} + 2q^{80} + 9q^{81} + 10q^{82} + 12q^{83} + 32q^{84} + 2q^{85} + 4q^{86} + 16q^{87} + 12q^{88} + 10q^{89} - 2q^{90} - 8q^{91} - 32q^{92} + 24q^{93} - 24q^{94} - 20q^{96} + 26q^{97} - 9q^{98} - 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$

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
17.2.a $$\chi_{17}(1, \cdot)$$ 17.2.a.a 1 1
17.2.b $$\chi_{17}(16, \cdot)$$ None 0 1
17.2.c $$\chi_{17}(4, \cdot)$$ None 0 2
17.2.d $$\chi_{17}(2, \cdot)$$ 17.2.d.a 4 4