# Properties

 Label 60.2 Level 60 Weight 2 Dimension 34 Nonzero newspaces 5 Newform subspaces 6 Sturm bound 384 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$5$$ Newform subspaces: $$6$$ Sturm bound: $$384$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(60))$$.

Total New Old
Modular forms 136 42 94
Cusp forms 57 34 23
Eisenstein series 79 8 71

## Trace form

 $$34 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 12 q^{8} - 10 q^{9} + O(q^{10})$$ $$34 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 12 q^{8} - 10 q^{9} - 20 q^{10} - 8 q^{11} - 4 q^{12} - 24 q^{13} - 14 q^{15} - 20 q^{17} + 16 q^{18} + 20 q^{20} - 12 q^{21} + 8 q^{22} + 24 q^{24} - 14 q^{25} + 16 q^{26} + 14 q^{27} + 24 q^{28} + 12 q^{29} + 36 q^{30} + 24 q^{31} + 20 q^{32} + 12 q^{33} + 24 q^{34} + 16 q^{35} + 16 q^{38} + 16 q^{40} - 4 q^{41} + 8 q^{42} - 12 q^{43} - 2 q^{45} - 24 q^{46} - 20 q^{48} - 18 q^{49} - 16 q^{50} - 12 q^{51} - 40 q^{52} + 4 q^{53} - 56 q^{54} - 8 q^{55} - 64 q^{56} + 20 q^{57} - 56 q^{58} - 8 q^{59} - 64 q^{60} - 36 q^{61} - 56 q^{62} + 8 q^{63} - 56 q^{64} + 20 q^{65} - 64 q^{66} - 4 q^{67} - 16 q^{68} + 32 q^{69} - 8 q^{70} + 12 q^{72} + 48 q^{73} + 2 q^{75} + 32 q^{76} + 48 q^{77} + 16 q^{78} + 24 q^{79} + 4 q^{80} + 26 q^{81} + 56 q^{82} + 56 q^{84} + 56 q^{85} + 64 q^{86} + 20 q^{87} + 104 q^{88} + 20 q^{89} + 60 q^{90} + 24 q^{91} + 56 q^{92} + 24 q^{93} + 104 q^{94} + 64 q^{96} - 32 q^{97} + 24 q^{98} + 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$

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
60.2.a $$\chi_{60}(1, \cdot)$$ None 0 1
60.2.d $$\chi_{60}(49, \cdot)$$ 60.2.d.a 2 1
60.2.e $$\chi_{60}(11, \cdot)$$ 60.2.e.a 8 1
60.2.h $$\chi_{60}(59, \cdot)$$ 60.2.h.a 4 1
60.2.h.b 4
60.2.i $$\chi_{60}(17, \cdot)$$ 60.2.i.a 4 2
60.2.j $$\chi_{60}(7, \cdot)$$ 60.2.j.a 12 2

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(60))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(60)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 2}$$