# Properties

 Label 118.2 Level 118 Weight 2 Dimension 144 Nonzero newspaces 2 Newforms 6 Sturm bound 1740 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$118 = 2 \cdot 59$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newforms: $$6$$ Sturm bound: $$1740$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(118))$$.

Total New Old
Modular forms 493 144 349
Cusp forms 378 144 234
Eisenstein series 115 0 115

## Trace form

 $$144q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} + O(q^{10})$$ $$144q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} - 6q^{10} - 12q^{11} - 4q^{12} - 14q^{13} - 8q^{14} - 24q^{15} - q^{16} - 18q^{17} - 13q^{18} - 20q^{19} - 6q^{20} - 32q^{21} - 12q^{22} - 24q^{23} - 4q^{24} - 31q^{25} - 14q^{26} - 40q^{27} - 8q^{28} - 30q^{29} - 24q^{30} - 32q^{31} - q^{32} - 48q^{33} - 18q^{34} - 48q^{35} - 13q^{36} - 38q^{37} - 20q^{38} - 56q^{39} - 6q^{40} - 42q^{41} - 32q^{42} - 44q^{43} - 12q^{44} - 20q^{45} + 34q^{46} + 10q^{47} - 4q^{48} + 59q^{49} + 85q^{50} + 160q^{51} + 44q^{52} + 62q^{53} + 163q^{54} + 102q^{55} - 8q^{56} + 210q^{57} + 28q^{58} + 57q^{59} + 150q^{60} + 54q^{61} + 26q^{62} + 186q^{63} - q^{64} + 90q^{65} + 155q^{66} + 48q^{67} + 40q^{68} + 136q^{69} + 68q^{70} + 44q^{71} - 13q^{72} - 16q^{73} + 20q^{74} - 66q^{75} - 20q^{76} - 96q^{77} - 56q^{78} - 80q^{79} - 6q^{80} - 121q^{81} - 42q^{82} - 84q^{83} - 32q^{84} - 108q^{85} - 44q^{86} - 120q^{87} - 12q^{88} - 90q^{89} - 78q^{90} - 112q^{91} - 24q^{92} - 128q^{93} - 48q^{94} - 120q^{95} - 4q^{96} - 98q^{97} - 57q^{98} - 69q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(118))$$

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
118.2.a $$\chi_{118}(1, \cdot)$$ 118.2.a.a 1 1
118.2.a.b 1
118.2.a.c 1
118.2.a.d 1
118.2.c $$\chi_{118}(3, \cdot)$$ 118.2.c.a 56 28
118.2.c.b 84

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(118))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(118)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 2}$$