## Defining parameters

 Level: $$N$$ = $$59$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newforms: $$2$$ Sturm bound: $$580$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(59))$$.

Total New Old
Modular forms 174 174 0
Cusp forms 117 117 0
Eisenstein series 57 57 0

## Trace form

 $$117q - 26q^{2} - 25q^{3} - 22q^{4} - 23q^{5} - 17q^{6} - 21q^{7} - 14q^{8} - 16q^{9} + O(q^{10})$$ $$117q - 26q^{2} - 25q^{3} - 22q^{4} - 23q^{5} - 17q^{6} - 21q^{7} - 14q^{8} - 16q^{9} - 11q^{10} - 17q^{11} - q^{12} - 15q^{13} - 5q^{14} - 5q^{15} + 2q^{16} - 11q^{17} + 10q^{18} - 9q^{19} + 13q^{20} + 3q^{21} + 7q^{22} - 5q^{23} + 31q^{24} + 2q^{25} + 13q^{26} + 11q^{27} + 27q^{28} + q^{29} + 43q^{30} + 3q^{31} + 34q^{32} + 19q^{33} + 25q^{34} + 19q^{35} + 62q^{36} + 9q^{37} + 31q^{38} + 27q^{39} + 61q^{40} + 13q^{41} + 67q^{42} + 15q^{43} + 55q^{44} + 20q^{45} - 15q^{46} - 10q^{47} - 79q^{48} - 30q^{49} - 52q^{50} - 73q^{51} - 47q^{52} - 33q^{53} - 112q^{54} - 44q^{55} - 141q^{56} - 94q^{57} - 26q^{58} - 28q^{59} - 238q^{60} - 25q^{61} + 9q^{62} - 70q^{63} - 134q^{64} - 32q^{65} - 88q^{66} - 19q^{67} - 19q^{68} - 49q^{69} - q^{70} - 15q^{71} - 8q^{72} + 16q^{73} + 27q^{74} + 66q^{75} + 111q^{76} + 67q^{77} + 139q^{78} + 51q^{79} + 157q^{80} + 92q^{81} + 97q^{82} + 55q^{83} + 195q^{84} + 79q^{85} + 103q^{86} + 91q^{87} + 151q^{88} + 61q^{89} + 205q^{90} + 83q^{91} + 139q^{92} + 99q^{93} + 115q^{94} + 91q^{95} + 223q^{96} + 69q^{97} + 55q^{98} + 40q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(59))$$

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
59.2.a $$\chi_{59}(1, \cdot)$$ 59.2.a.a 5 1
59.2.c $$\chi_{59}(3, \cdot)$$ 59.2.c.a 112 28