## Defining parameters

 Level: $$N$$ = $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Newform subspaces: $$18$$ Sturm bound: $$3072$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(160))$$.

Total New Old
Modular forms 896 426 470
Cusp forms 641 366 275
Eisenstein series 255 60 195

## Trace form

 $$366q - 8q^{2} - 4q^{3} - 8q^{4} - 10q^{5} - 24q^{6} - 4q^{7} - 8q^{8} - 10q^{9} + O(q^{10})$$ $$366q - 8q^{2} - 4q^{3} - 8q^{4} - 10q^{5} - 24q^{6} - 4q^{7} - 8q^{8} - 10q^{9} - 20q^{10} - 16q^{11} - 40q^{12} - 20q^{13} - 40q^{14} - 12q^{15} - 64q^{16} - 12q^{17} - 48q^{18} - 8q^{19} - 28q^{20} - 24q^{21} - 32q^{22} - 20q^{23} + 16q^{24} - 14q^{25} + 16q^{26} - 64q^{27} + 32q^{28} + 4q^{29} + 20q^{30} - 72q^{31} + 32q^{32} - 56q^{33} + 16q^{34} - 56q^{35} + 32q^{36} - 44q^{37} - 24q^{38} - 80q^{39} - 24q^{40} - 92q^{41} - 48q^{42} - 52q^{43} - 88q^{44} - 70q^{45} - 88q^{46} - 36q^{47} - 112q^{48} - 26q^{49} - 52q^{50} - 24q^{51} - 24q^{52} - 76q^{53} - 32q^{54} + 4q^{55} - 48q^{56} + 8q^{57} + 56q^{59} + 56q^{60} - 68q^{61} + 32q^{62} + 100q^{63} + 112q^{64} + 12q^{65} + 152q^{66} + 100q^{67} + 64q^{68} + 24q^{69} + 144q^{70} + 80q^{71} + 184q^{72} + 60q^{73} + 136q^{74} + 80q^{75} + 104q^{76} + 56q^{77} + 216q^{78} + 48q^{79} + 152q^{80} + 94q^{81} + 152q^{82} - 44q^{83} + 256q^{84} + 68q^{85} + 144q^{86} - 72q^{87} + 160q^{88} + 28q^{89} + 216q^{90} - 80q^{91} + 208q^{92} + 112q^{93} + 80q^{94} - 64q^{95} + 96q^{96} - 28q^{97} + 80q^{98} - 112q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$

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
160.2.a $$\chi_{160}(1, \cdot)$$ 160.2.a.a 1 1
160.2.a.b 1
160.2.a.c 2
160.2.c $$\chi_{160}(129, \cdot)$$ 160.2.c.a 2 1
160.2.c.b 4
160.2.d $$\chi_{160}(81, \cdot)$$ 160.2.d.a 4 1
160.2.f $$\chi_{160}(49, \cdot)$$ 160.2.f.a 4 1
160.2.j $$\chi_{160}(87, \cdot)$$ None 0 2
160.2.l $$\chi_{160}(41, \cdot)$$ None 0 2
160.2.n $$\chi_{160}(63, \cdot)$$ 160.2.n.a 2 2
160.2.n.b 2
160.2.n.c 2
160.2.n.d 2
160.2.n.e 2
160.2.n.f 2
160.2.o $$\chi_{160}(47, \cdot)$$ 160.2.o.a 8 2
160.2.q $$\chi_{160}(9, \cdot)$$ None 0 2
160.2.s $$\chi_{160}(7, \cdot)$$ None 0 2
160.2.u $$\chi_{160}(43, \cdot)$$ 160.2.u.a 88 4
160.2.x $$\chi_{160}(21, \cdot)$$ 160.2.x.a 64 4
160.2.z $$\chi_{160}(29, \cdot)$$ 160.2.z.a 88 4
160.2.ba $$\chi_{160}(3, \cdot)$$ 160.2.ba.a 88 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(160))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(160)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$