## Defining parameters

 Level: $$N$$ = $$35 = 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$8$$ Sturm bound: $$192$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(35))$$.

Total New Old
Modular forms 72 57 15
Cusp forms 25 25 0
Eisenstein series 47 32 15

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$

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
35.2.a $$\chi_{35}(1, \cdot)$$ 35.2.a.a 1 1
35.2.a.b 2
35.2.b $$\chi_{35}(29, \cdot)$$ 35.2.b.a 2 1
35.2.e $$\chi_{35}(11, \cdot)$$ 35.2.e.a 4 2
35.2.f $$\chi_{35}(13, \cdot)$$ 35.2.f.a 4 2
35.2.j $$\chi_{35}(4, \cdot)$$ 35.2.j.a 4 2
35.2.k $$\chi_{35}(3, \cdot)$$ 35.2.k.a 4 4
35.2.k.b 4