# Properties

 Label 62.2 Level 62 Weight 2 Dimension 39 Nonzero newspaces 4 Newform subspaces 8 Sturm bound 480 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$62 = 2 \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$8$$ Sturm bound: $$480$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(62))$$.

Total New Old
Modular forms 150 39 111
Cusp forms 91 39 52
Eisenstein series 59 0 59

## Trace form

 $$39q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} + O(q^{10})$$ $$39q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} - 6q^{10} - 12q^{11} - 4q^{12} - 14q^{13} - 8q^{14} - 24q^{15} - q^{16} - 18q^{17} - 13q^{18} - 20q^{19} - 6q^{20} - 22q^{21} + 18q^{22} + 6q^{23} - 4q^{24} + 39q^{25} + 16q^{26} + 50q^{27} + 32q^{28} + 30q^{29} + 36q^{30} + 29q^{31} - q^{32} + 12q^{33} + 42q^{34} + 12q^{35} + 27q^{36} + 52q^{37} + 10q^{38} + 14q^{39} - 6q^{40} - 12q^{41} - 2q^{42} - 34q^{43} - 12q^{44} - 78q^{45} - 24q^{46} - 48q^{47} - 4q^{48} - 27q^{49} - 31q^{50} + 18q^{51} - 14q^{52} - 24q^{53} - 40q^{54} - 12q^{55} - 8q^{56} + 10q^{57} - 30q^{58} - 30q^{59} - 24q^{60} + 28q^{61} - 31q^{62} + 16q^{63} - q^{64} + 6q^{65} - 48q^{66} - 38q^{67} - 18q^{68} - 6q^{69} - 48q^{70} - 12q^{71} - 13q^{72} - 44q^{73} - 38q^{74} - 4q^{75} - 10q^{76} + 24q^{77} + 34q^{78} - 10q^{79} + 24q^{80} - q^{81} + 18q^{82} + 126q^{83} + 28q^{84} + 12q^{85} + 76q^{86} + 48q^{88} + 60q^{89} + 102q^{90} + 18q^{91} - 24q^{92} + 116q^{93} + 12q^{94} + 120q^{95} - 4q^{96} + 32q^{97} + 123q^{98} - 6q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$

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
62.2.a $$\chi_{62}(1, \cdot)$$ 62.2.a.a 1 1
62.2.a.b 2
62.2.c $$\chi_{62}(5, \cdot)$$ 62.2.c.a 2 2
62.2.c.b 2
62.2.d $$\chi_{62}(33, \cdot)$$ 62.2.d.a 8 4
62.2.d.b 8
62.2.g $$\chi_{62}(7, \cdot)$$ 62.2.g.a 8 8
62.2.g.b 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(62))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(62)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 2}$$