## Defining parameters

 Level: $$N$$ = $$134 = 2 \cdot 67$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newforms: $$9$$ Sturm bound: $$2244$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(134))$$.

Total New Old
Modular forms 627 186 441
Cusp forms 496 186 310
Eisenstein series 131 0 131

## Trace form

 $$186q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} + O(q^{10})$$ $$186q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} - 6q^{10} - 12q^{11} - 4q^{12} - 14q^{13} - 8q^{14} - 24q^{15} - q^{16} - 18q^{17} - 13q^{18} - 20q^{19} - 6q^{20} - 32q^{21} - 12q^{22} - 24q^{23} - 4q^{24} - 31q^{25} - 14q^{26} - 40q^{27} - 8q^{28} - 30q^{29} - 24q^{30} - 32q^{31} - q^{32} - 48q^{33} - 18q^{34} - 48q^{35} - 13q^{36} - 38q^{37} - 20q^{38} - 56q^{39} - 6q^{40} - 42q^{41} - 32q^{42} - 44q^{43} - 12q^{44} - 78q^{45} - 24q^{46} - 48q^{47} - 4q^{48} - 57q^{49} - 31q^{50} - 72q^{51} + 8q^{52} + 12q^{53} + 59q^{54} + 126q^{55} - 8q^{56} + 74q^{57} + 102q^{58} + 72q^{59} + 108q^{60} + 202q^{61} + 34q^{62} + 182q^{63} - q^{64} + 180q^{65} + 216q^{66} + 65q^{67} + 48q^{68} + 36q^{69} + 216q^{70} + 192q^{71} - 13q^{72} + 212q^{73} + 28q^{74} + 140q^{75} + 112q^{76} + 36q^{77} + 76q^{78} + 74q^{79} - 6q^{80} + 77q^{81} + 57q^{82} - 18q^{83} - 10q^{84} - 108q^{85} - 44q^{86} - 120q^{87} - 12q^{88} - 90q^{89} - 78q^{90} - 112q^{91} - 24q^{92} - 128q^{93} - 48q^{94} - 120q^{95} - 4q^{96} - 98q^{97} - 57q^{98} - 156q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(134))$$

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
134.2.a $$\chi_{134}(1, \cdot)$$ 134.2.a.a 3 1
134.2.a.b 3
134.2.c $$\chi_{134}(29, \cdot)$$ 134.2.c.a 2 2
134.2.c.b 4
134.2.c.c 4
134.2.e $$\chi_{134}(9, \cdot)$$ 134.2.e.a 30 10
134.2.e.b 40
134.2.g $$\chi_{134}(17, \cdot)$$ 134.2.g.a 40 20
134.2.g.b 60

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(134))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(134)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(67))$$$$^{\oplus 2}$$