# Properties

 Label 35.2 Level 35 Weight 2 Dimension 25 Nonzero newspaces 6 Newform subspaces 8 Sturm bound 192 Trace bound 2

## 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

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

## 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