## 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

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

## 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