## 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

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

## 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

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