## Defining parameters

 Level: $$N$$ = $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$10$$ Newform subspaces: $$19$$ Sturm bound: $$4608$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(160))$$.

Total New Old
Modular forms 1664 822 842
Cusp forms 1408 762 646
Eisenstein series 256 60 196

## Trace form

 $$762q - 8q^{2} - 8q^{3} - 8q^{4} - 16q^{5} - 24q^{6} - 4q^{7} - 8q^{8} + 22q^{9} + O(q^{10})$$ $$762q - 8q^{2} - 8q^{3} - 8q^{4} - 16q^{5} - 24q^{6} - 4q^{7} - 8q^{8} + 22q^{9} + 28q^{10} + 12q^{11} + 88q^{12} + 48q^{13} + 24q^{14} - 4q^{15} - 64q^{16} - 84q^{17} - 128q^{18} - 68q^{19} - 92q^{20} - 152q^{21} - 304q^{22} + 124q^{23} - 432q^{24} + 22q^{25} - 224q^{26} + 280q^{27} - 128q^{28} + 128q^{29} - 36q^{30} + 104q^{31} + 32q^{32} + 160q^{33} + 80q^{34} - 8q^{35} + 640q^{36} + 192q^{37} + 776q^{38} - 392q^{39} + 392q^{40} + 44q^{41} + 832q^{42} - 296q^{43} + 360q^{44} - 188q^{45} + 40q^{46} - 188q^{47} - 112q^{48} - 366q^{49} - 324q^{50} - 672q^{51} - 856q^{52} - 64q^{53} - 1200q^{54} - 364q^{55} - 1136q^{56} - 416q^{57} - 1072q^{58} - 420q^{59} - 712q^{60} - 224q^{61} - 448q^{62} - 244q^{63} - 272q^{64} - 424q^{65} - 536q^{66} + 152q^{67} - 512q^{68} - 712q^{69} - 648q^{70} + 240q^{71} - 200q^{72} - 380q^{73} + 168q^{74} + 52q^{75} + 616q^{76} - 520q^{77} + 152q^{78} + 1008q^{79} - 168q^{80} + 642q^{81} - 808q^{82} + 1432q^{83} - 480q^{84} + 392q^{85} - 512q^{86} + 1376q^{87} + 224q^{88} + 452q^{89} + 1752q^{90} + 752q^{91} + 624q^{92} + 752q^{93} + 1584q^{94} + 472q^{95} + 2400q^{96} + 796q^{97} + 1552q^{98} + 68q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(160))$$

We only show spaces with odd 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
160.3.b $$\chi_{160}(31, \cdot)$$ 160.3.b.a 4 1
160.3.b.b 4
160.3.e $$\chi_{160}(79, \cdot)$$ 160.3.e.a 1 1
160.3.e.b 1
160.3.e.c 8
160.3.g $$\chi_{160}(111, \cdot)$$ 160.3.g.a 8 1
160.3.h $$\chi_{160}(159, \cdot)$$ 160.3.h.a 6 1
160.3.h.b 6
160.3.i $$\chi_{160}(57, \cdot)$$ None 0 2
160.3.k $$\chi_{160}(39, \cdot)$$ None 0 2
160.3.m $$\chi_{160}(17, \cdot)$$ 160.3.m.a 20 2
160.3.p $$\chi_{160}(33, \cdot)$$ 160.3.p.a 2 2
160.3.p.b 2
160.3.p.c 4
160.3.p.d 4
160.3.p.e 6
160.3.p.f 6
160.3.r $$\chi_{160}(71, \cdot)$$ None 0 2
160.3.t $$\chi_{160}(137, \cdot)$$ None 0 2
160.3.v $$\chi_{160}(13, \cdot)$$ 160.3.v.a 184 4
160.3.w $$\chi_{160}(11, \cdot)$$ 160.3.w.a 128 4
160.3.y $$\chi_{160}(19, \cdot)$$ 160.3.y.a 184 4
160.3.bb $$\chi_{160}(53, \cdot)$$ 160.3.bb.a 184 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(160))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(160)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$