# Properties

 Label 154.2 Level 154 Weight 2 Dimension 229 Nonzero newspaces 8 Newform subspaces 22 Sturm bound 2880 Trace bound 4

## 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

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(154)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 1}$$