# Properties

 Label 55.2 Level 55 Weight 2 Dimension 79 Nonzero newspaces 6 Newform subspaces 9 Sturm bound 480 Trace bound 2

## 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

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

## 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

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