## Defining parameters

 Level: $$N$$ = $$161 = 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$15$$ Sturm bound: $$4224$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(161))$$.

Total New Old
Modular forms 1188 1113 75
Cusp forms 925 901 24
Eisenstein series 263 212 51

## Trace form

 $$901q - 47q^{2} - 48q^{3} - 51q^{4} - 50q^{5} - 56q^{6} - 56q^{7} - 125q^{8} - 57q^{9} + O(q^{10})$$ $$901q - 47q^{2} - 48q^{3} - 51q^{4} - 50q^{5} - 56q^{6} - 56q^{7} - 125q^{8} - 57q^{9} - 62q^{10} - 56q^{11} - 72q^{12} - 58q^{13} - 58q^{14} - 112q^{15} - 31q^{16} - 40q^{17} + 5q^{18} - 42q^{19} + 2q^{20} - 26q^{21} - 80q^{22} - 23q^{23} - 16q^{24} - 31q^{25} - 42q^{26} - 18q^{27} - 18q^{28} - 118q^{29} - 28q^{30} - 54q^{31} - 63q^{32} - 70q^{33} - 54q^{34} - 39q^{35} - 91q^{36} + 6q^{37} + 6q^{38} - 12q^{39} + 42q^{40} - 42q^{41} + 43q^{42} - 66q^{43} + 70q^{44} + 32q^{45} + 63q^{46} - 48q^{47} + 52q^{48} + 10q^{49} - 49q^{50} - 28q^{51} + 78q^{52} - 54q^{53} + 56q^{54} + 16q^{55} + 51q^{56} - 36q^{57} + 64q^{58} + 28q^{59} + 52q^{60} - 18q^{61} - 8q^{62} - 13q^{63} - 61q^{64} + 26q^{65} + 54q^{66} - 68q^{67} + 116q^{68} - 26q^{69} - 40q^{70} - 72q^{71} + 91q^{72} - 74q^{73} + 40q^{74} + 74q^{75} + 102q^{76} + 32q^{77} + 74q^{78} + 52q^{79} + 188q^{80} + 187q^{81} + 50q^{82} + 26q^{83} + 137q^{84} + 46q^{85} + 88q^{86} + 100q^{87} + 40q^{88} - 2q^{89} + 184q^{90} + 30q^{91} - 73q^{92} + 48q^{93} + 54q^{94} + 34q^{95} + 298q^{96} + 56q^{97} - 3q^{98} + 108q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$

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
161.2.a $$\chi_{161}(1, \cdot)$$ 161.2.a.a 1 1
161.2.a.b 2
161.2.a.c 3
161.2.a.d 5
161.2.c $$\chi_{161}(160, \cdot)$$ 161.2.c.a 2 1
161.2.c.b 12
161.2.e $$\chi_{161}(93, \cdot)$$ 161.2.e.a 14 2
161.2.e.b 14
161.2.g $$\chi_{161}(45, \cdot)$$ 161.2.g.a 28 2
161.2.i $$\chi_{161}(8, \cdot)$$ 161.2.i.a 50 10
161.2.i.b 70
161.2.k $$\chi_{161}(20, \cdot)$$ 161.2.k.a 20 10
161.2.k.b 120
161.2.m $$\chi_{161}(2, \cdot)$$ 161.2.m.a 280 20
161.2.o $$\chi_{161}(5, \cdot)$$ 161.2.o.a 280 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(161))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(161)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 2}$$