## Defining parameters

 Level: $$N$$ = $$55 = 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$9$$ Sturm bound: $$480$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(55))$$.

Total New Old
Modular forms 160 135 25
Cusp forms 81 79 2
Eisenstein series 79 56 23

## Trace form

 $$79q - 13q^{2} - 14q^{3} - 17q^{4} - 16q^{5} - 32q^{6} - 8q^{7} - 5q^{8} - 3q^{9} + O(q^{10})$$ $$79q - 13q^{2} - 14q^{3} - 17q^{4} - 16q^{5} - 32q^{6} - 8q^{7} - 5q^{8} - 3q^{9} - 3q^{10} - 31q^{11} - 8q^{12} - 14q^{13} - 4q^{14} + q^{15} - q^{16} + 2q^{17} + 11q^{18} + 13q^{20} - 12q^{21} + 17q^{22} - 14q^{23} + 40q^{24} + 14q^{25} + 18q^{26} + 10q^{27} + 44q^{28} + 10q^{29} + 38q^{30} - 22q^{31} + 27q^{32} + 26q^{33} + 6q^{34} + 22q^{35} + 59q^{36} + 12q^{37} + 40q^{38} + 44q^{39} - 25q^{40} + 18q^{41} + 44q^{42} - 4q^{43} - 27q^{44} - 33q^{45} - 52q^{46} - 48q^{47} - 64q^{48} - 57q^{49} - 43q^{50} - 52q^{51} - 98q^{52} - 14q^{53} - 60q^{54} - 46q^{55} - 120q^{56} - 20q^{57} - 90q^{58} - 30q^{59} - 38q^{60} - 82q^{61} + 24q^{62} - 24q^{63} - 37q^{64} - 14q^{65} + 8q^{66} - 18q^{67} + 34q^{68} + 34q^{69} + 56q^{70} + 38q^{71} + 55q^{72} + 46q^{73} + 106q^{74} + 71q^{75} + 100q^{76} + 72q^{77} + 112q^{78} + 80q^{79} + 139q^{80} + 79q^{81} + 74q^{82} + 76q^{83} + 116q^{84} + 72q^{85} + 68q^{86} + 100q^{87} + 145q^{88} + 20q^{89} - 9q^{90} + 48q^{91} + 52q^{92} + 2q^{93} + 16q^{94} - 52q^{96} - 28q^{97} - 81q^{98} - 73q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$

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
55.2.a $$\chi_{55}(1, \cdot)$$ 55.2.a.a 1 1
55.2.a.b 2
55.2.b $$\chi_{55}(34, \cdot)$$ 55.2.b.a 4 1
55.2.e $$\chi_{55}(32, \cdot)$$ 55.2.e.a 4 2
55.2.e.b 4
55.2.g $$\chi_{55}(16, \cdot)$$ 55.2.g.a 8 4
55.2.g.b 8
55.2.j $$\chi_{55}(4, \cdot)$$ 55.2.j.a 16 4
55.2.l $$\chi_{55}(2, \cdot)$$ 55.2.l.a 32 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(55))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(55)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$