## Defining parameters

 Level: $$N$$ = $$154 = 2 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$22$$ Sturm bound: $$2880$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(154))$$.

Total New Old
Modular forms 840 229 611
Cusp forms 601 229 372
Eisenstein series 239 0 239

## Trace form

 $$229q + 3q^{2} + 8q^{3} - q^{4} + 6q^{5} - 10q^{6} - 11q^{7} + 3q^{8} - 29q^{9} + O(q^{10})$$ $$229q + 3q^{2} + 8q^{3} - q^{4} + 6q^{5} - 10q^{6} - 11q^{7} + 3q^{8} - 29q^{9} - 14q^{10} - 9q^{11} - 12q^{12} + 2q^{13} - 7q^{14} - 36q^{15} - q^{16} - 34q^{17} + 5q^{18} - 14q^{19} + 6q^{20} - 12q^{21} + 11q^{22} - 16q^{23} - 10q^{24} - 39q^{25} - 34q^{26} - 58q^{27} - 11q^{28} - 38q^{29} - 36q^{30} - 20q^{31} - 7q^{32} - 66q^{33} - 10q^{34} - 54q^{35} + q^{36} - 6q^{37} - 36q^{38} - 60q^{39} - 14q^{40} - 50q^{41} - 30q^{42} - 72q^{43} - 19q^{44} - 22q^{45} - 16q^{46} - 8q^{47} + 8q^{48} - 61q^{49} - 19q^{50} - 34q^{51} - 18q^{52} - 58q^{53} - 32q^{54} - 74q^{55} + 3q^{56} - 82q^{57} - 62q^{58} - 58q^{59} - 16q^{60} - 34q^{61} + 24q^{62} + 71q^{63} - q^{64} + 64q^{65} + 164q^{66} + 16q^{67} + 26q^{68} + 176q^{69} + 146q^{70} + 152q^{71} + 95q^{72} + 130q^{73} + 122q^{74} + 354q^{75} + 56q^{76} + 111q^{77} + 232q^{78} + 144q^{79} + 46q^{80} + 353q^{81} + 104q^{82} + 146q^{83} + 88q^{84} + 128q^{85} + 110q^{86} + 196q^{87} + 51q^{88} + 62q^{89} + 138q^{90} + 102q^{91} - 36q^{92} + 32q^{93} - 36q^{94} - 40q^{95} - 72q^{97} - 7q^{98} - 117q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$

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
154.2.a $$\chi_{154}(1, \cdot)$$ 154.2.a.a 1 1
154.2.a.b 1
154.2.a.c 1
154.2.a.d 2
154.2.c $$\chi_{154}(153, \cdot)$$ 154.2.c.a 8 1
154.2.e $$\chi_{154}(23, \cdot)$$ 154.2.e.a 2 2
154.2.e.b 2
154.2.e.c 2
154.2.e.d 2
154.2.e.e 4
154.2.e.f 4
154.2.f $$\chi_{154}(15, \cdot)$$ 154.2.f.a 4 4
154.2.f.b 4
154.2.f.c 4
154.2.f.d 4
154.2.f.e 8
154.2.i $$\chi_{154}(87, \cdot)$$ 154.2.i.a 16 2
154.2.k $$\chi_{154}(13, \cdot)$$ 154.2.k.a 32 4
154.2.m $$\chi_{154}(9, \cdot)$$ 154.2.m.a 8 8
154.2.m.b 24
154.2.m.c 32
154.2.n $$\chi_{154}(17, \cdot)$$ 154.2.n.a 64 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(154))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(154)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 2}$$