# Properties

 Label 110.2 Level 110 Weight 2 Dimension 111 Nonzero newspaces 6 Newforms 16 Sturm bound 1440 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$110 = 2 \cdot 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newforms: $$16$$ Sturm bound: $$1440$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(110))$$.

Total New Old
Modular forms 440 111 329
Cusp forms 281 111 170
Eisenstein series 159 0 159

## Trace form

 $$111q + q^{2} + 4q^{3} + q^{4} + q^{5} - 6q^{6} - 12q^{7} + q^{8} - 27q^{9} + O(q^{10})$$ $$111q + q^{2} + 4q^{3} + q^{4} + q^{5} - 6q^{6} - 12q^{7} + q^{8} - 27q^{9} - 9q^{10} - 9q^{11} - 16q^{12} - 6q^{13} - 12q^{14} - 26q^{15} + q^{16} - 22q^{17} + 3q^{18} - 10q^{19} + q^{20} - 8q^{21} + 11q^{22} - 16q^{23} - 6q^{24} - 39q^{25} - 26q^{26} - 50q^{27} - 12q^{28} - 50q^{29} - 26q^{30} - 28q^{31} - 9q^{32} - 66q^{33} - 22q^{34} - 52q^{35} + 3q^{36} - 2q^{37} - 40q^{38} - 44q^{39} - 9q^{40} - 38q^{41} + 12q^{42} + 24q^{43} + 21q^{44} + 83q^{45} + 64q^{46} + 88q^{47} + 4q^{48} + 137q^{49} + 61q^{50} + 102q^{51} + 54q^{52} + 74q^{53} + 120q^{54} + 101q^{55} + 8q^{56} + 70q^{57} + 110q^{58} + 50q^{59} + 64q^{60} + 82q^{61} + 52q^{62} + 64q^{63} + q^{64} + 34q^{65} + 4q^{66} + 8q^{67} + 18q^{68} - 44q^{69} + 8q^{70} - 88q^{71} - 27q^{72} - 46q^{73} - 2q^{74} - 86q^{75} - 72q^{77} - 24q^{78} - 20q^{79} - 9q^{80} - 149q^{81} - 28q^{82} - 46q^{83} - 48q^{84} - 92q^{85} - 86q^{86} - 80q^{87} - 9q^{88} - 70q^{89} - 77q^{90} - 48q^{91} - 36q^{92} - 12q^{93} - 72q^{94} - 10q^{95} + 4q^{96} + 28q^{97} - 33q^{98} + 83q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$

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
110.2.a $$\chi_{110}(1, \cdot)$$ 110.2.a.a 1 1
110.2.a.b 1
110.2.a.c 1
110.2.a.d 2
110.2.b $$\chi_{110}(89, \cdot)$$ 110.2.b.a 2 1
110.2.b.b 2
110.2.b.c 2
110.2.f $$\chi_{110}(43, \cdot)$$ 110.2.f.a 4 2
110.2.f.b 4
110.2.f.c 4
110.2.g $$\chi_{110}(31, \cdot)$$ 110.2.g.a 4 4
110.2.g.b 4
110.2.g.c 8
110.2.j $$\chi_{110}(9, \cdot)$$ 110.2.j.a 8 4
110.2.j.b 16
110.2.k $$\chi_{110}(7, \cdot)$$ 110.2.k.a 48 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(110))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(110)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$