# Properties

 Label 155.2 Level 155 Weight 2 Dimension 789 Nonzero newspaces 12 Newform subspaces 25 Sturm bound 3840 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$155 = 5 \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$25$$ Sturm bound: $$3840$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(155))$$.

Total New Old
Modular forms 1080 965 115
Cusp forms 841 789 52
Eisenstein series 239 176 63

## Trace form

 $$789q - 33q^{2} - 34q^{3} - 37q^{4} - 46q^{5} - 102q^{6} - 38q^{7} - 45q^{8} - 43q^{9} + O(q^{10})$$ $$789q - 33q^{2} - 34q^{3} - 37q^{4} - 46q^{5} - 102q^{6} - 38q^{7} - 45q^{8} - 43q^{9} - 48q^{10} - 102q^{11} - 58q^{12} - 44q^{13} - 54q^{14} - 49q^{15} - 121q^{16} - 48q^{17} - 69q^{18} - 50q^{19} - 52q^{20} - 112q^{21} - 6q^{22} - 24q^{23} + 30q^{24} - 36q^{25} - 72q^{26} + 20q^{27} + 74q^{28} + 18q^{30} - 61q^{31} + 57q^{32} - 18q^{33} + 36q^{34} - 23q^{35} - 21q^{36} + 22q^{37} - 30q^{38} - 16q^{39} - 102q^{41} - 66q^{42} - 64q^{43} - 114q^{44} - 58q^{45} - 162q^{46} - 78q^{47} - 64q^{48} - 27q^{49} + 27q^{50} + 18q^{51} + 22q^{52} - 24q^{53} + 180q^{54} + 3q^{55} + 60q^{56} + 70q^{57} + 90q^{58} - 30q^{59} + 182q^{60} + 58q^{61} + 57q^{62} + 76q^{63} + 83q^{64} + 31q^{65} + 216q^{66} - 38q^{67} + 54q^{68} + 54q^{69} + 66q^{70} - 42q^{71} + 105q^{72} - 44q^{73} + 6q^{74} + 56q^{75} + 20q^{76} + 24q^{77} + 72q^{78} - 40q^{79} + 74q^{80} - 91q^{81} - 36q^{82} + 96q^{83} + 106q^{84} - 3q^{85} + 18q^{86} - 30q^{87} + 150q^{88} + 30q^{89} + 141q^{90} - 72q^{91} + 192q^{92} + 86q^{93} - 84q^{94} + 55q^{95} + 108q^{96} + 2q^{97} + 159q^{98} - 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$

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
155.2.a $$\chi_{155}(1, \cdot)$$ 155.2.a.a 1 1
155.2.a.b 1
155.2.a.c 1
155.2.a.d 4
155.2.a.e 4
155.2.b $$\chi_{155}(94, \cdot)$$ 155.2.b.a 4 1
155.2.b.b 10
155.2.e $$\chi_{155}(36, \cdot)$$ 155.2.e.a 2 2
155.2.e.b 2
155.2.e.c 8
155.2.e.d 8
155.2.f $$\chi_{155}(92, \cdot)$$ 155.2.f.a 12 2
155.2.f.b 16
155.2.h $$\chi_{155}(16, \cdot)$$ 155.2.h.a 24 4
155.2.h.b 24
155.2.j $$\chi_{155}(129, \cdot)$$ 155.2.j.a 28 2
155.2.n $$\chi_{155}(4, \cdot)$$ 155.2.n.a 56 4
155.2.p $$\chi_{155}(37, \cdot)$$ 155.2.p.a 4 4
155.2.p.b 4
155.2.p.c 48
155.2.q $$\chi_{155}(41, \cdot)$$ 155.2.q.a 40 8
155.2.q.b 40
155.2.r $$\chi_{155}(23, \cdot)$$ 155.2.r.a 112 8
155.2.u $$\chi_{155}(9, \cdot)$$ 155.2.u.a 112 8
155.2.x $$\chi_{155}(3, \cdot)$$ 155.2.x.a 224 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(155))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(155)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 2}$$