# Properties

 Label 57.2 Level 57 Weight 2 Dimension 71 Nonzero newspaces 6 Newform subspaces 11 Sturm bound 480 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$57 = 3 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$480$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(57))$$.

Total New Old
Modular forms 156 107 49
Cusp forms 85 71 14
Eisenstein series 71 36 35

## Trace form

 $$71 q - 3 q^{2} - 10 q^{3} - 25 q^{4} - 6 q^{5} - 12 q^{6} - 26 q^{7} - 15 q^{8} - 10 q^{9} + O(q^{10})$$ $$71 q - 3 q^{2} - 10 q^{3} - 25 q^{4} - 6 q^{5} - 12 q^{6} - 26 q^{7} - 15 q^{8} - 10 q^{9} - 36 q^{10} - 12 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} + 3 q^{15} + 23 q^{16} - 3 q^{18} + 5 q^{19} + 30 q^{20} + 4 q^{21} - 6 q^{23} + 12 q^{24} - 13 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 6 q^{29} + 36 q^{30} - 14 q^{31} + 27 q^{32} + 33 q^{33} + 18 q^{34} + 24 q^{35} + 56 q^{36} - 2 q^{37} + 69 q^{38} + 22 q^{39} + 54 q^{40} - 6 q^{41} + 57 q^{42} + 10 q^{43} + 6 q^{44} + 12 q^{45} - 12 q^{47} - 40 q^{48} - 39 q^{49} - 39 q^{50} - 63 q^{51} - 116 q^{52} - 54 q^{53} - 66 q^{54} - 90 q^{55} - 120 q^{56} - 73 q^{57} - 126 q^{58} - 60 q^{59} - 114 q^{60} - 20 q^{61} - 6 q^{62} - 41 q^{63} - q^{64} + 24 q^{65} - 45 q^{66} + 58 q^{67} + 12 q^{69} + 54 q^{70} + 39 q^{72} + 70 q^{73} + 30 q^{74} + 53 q^{75} + 29 q^{76} + 102 q^{77} + 93 q^{78} + 106 q^{79} + 66 q^{80} + 26 q^{81} + 198 q^{82} + 42 q^{83} + 151 q^{84} + 90 q^{85} + 66 q^{86} + 105 q^{87} + 126 q^{88} + 72 q^{89} + 36 q^{90} + 38 q^{91} + 66 q^{92} + 61 q^{93} + 36 q^{94} - 60 q^{95} - 9 q^{96} - 62 q^{97} - 27 q^{98} - 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
57.2.a $$\chi_{57}(1, \cdot)$$ 57.2.a.a 1 1
57.2.a.b 1
57.2.a.c 1
57.2.d $$\chi_{57}(56, \cdot)$$ 57.2.d.a 4 1
57.2.e $$\chi_{57}(7, \cdot)$$ 57.2.e.a 2 2
57.2.e.b 6
57.2.f $$\chi_{57}(8, \cdot)$$ 57.2.f.a 8 2
57.2.i $$\chi_{57}(4, \cdot)$$ 57.2.i.a 6 6
57.2.i.b 12
57.2.j $$\chi_{57}(2, \cdot)$$ 57.2.j.a 6 6
57.2.j.b 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(57))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(57)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 1}$$