## Defining parameters

 Level: $$N$$ = $$1610 = 2 \cdot 5 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$304128$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1610))$$.

Total New Old
Modular forms 78144 22173 55971
Cusp forms 73921 22173 51748
Eisenstein series 4223 0 4223

## Trace form

 $$22173q - 3q^{2} - 4q^{3} + 5q^{4} + 9q^{5} + 12q^{6} + 17q^{7} - 3q^{8} + 17q^{9} + O(q^{10})$$ $$22173q - 3q^{2} - 4q^{3} + 5q^{4} + 9q^{5} + 12q^{6} + 17q^{7} - 3q^{8} + 17q^{9} + 9q^{10} + 12q^{11} - 4q^{12} - 2q^{13} + 9q^{14} + 80q^{15} + 5q^{16} + 130q^{17} + 185q^{18} + 116q^{19} + 53q^{20} + 176q^{21} + 100q^{22} + 177q^{23} + 12q^{24} + 69q^{25} + 70q^{26} + 176q^{27} + 13q^{28} - 2q^{29} - 20q^{30} + 8q^{31} - 3q^{32} - 104q^{33} - 102q^{34} - 53q^{35} - 79q^{36} + 78q^{37} - 84q^{38} + 24q^{39} + 9q^{40} + 58q^{41} - 84q^{42} + 156q^{43} - 36q^{44} + 105q^{45} - 23q^{46} + 128q^{47} - 4q^{48} + 233q^{49} + 69q^{50} + 200q^{51} - 2q^{52} + 166q^{53} + 112q^{54} + 236q^{55} + 53q^{56} + 408q^{57} + 230q^{58} + 380q^{59} + 80q^{60} + 302q^{61} + 312q^{62} + 201q^{63} + 5q^{64} + 290q^{65} + 400q^{66} + 36q^{67} + 218q^{68} + 348q^{69} + 157q^{70} + 416q^{71} + 185q^{72} + 66q^{73} + 382q^{74} + 396q^{75} + 28q^{76} + 232q^{77} + 288q^{78} + 360q^{79} + 53q^{80} + 461q^{81} + 194q^{82} + 316q^{83} + 88q^{84} + 198q^{85} + 52q^{86} + 240q^{87} - 36q^{88} - 86q^{89} - 75q^{90} + 62q^{91} - 47q^{92} - 176q^{93} - 96q^{94} - 248q^{95} - 36q^{96} - 406q^{97} - 283q^{98} - 404q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1610))$$

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
1610.2.a $$\chi_{1610}(1, \cdot)$$ 1610.2.a.a 1 1
1610.2.a.b 1
1610.2.a.c 1
1610.2.a.d 1
1610.2.a.e 1
1610.2.a.f 1
1610.2.a.g 1
1610.2.a.h 2
1610.2.a.i 2
1610.2.a.j 2
1610.2.a.k 3
1610.2.a.l 3
1610.2.a.m 3
1610.2.a.n 3
1610.2.a.o 3
1610.2.a.p 4
1610.2.a.q 4
1610.2.a.r 4
1610.2.a.s 5
1610.2.c $$\chi_{1610}(321, \cdot)$$ 1610.2.c.a 4 1
1610.2.c.b 4
1610.2.c.c 4
1610.2.c.d 4
1610.2.c.e 12
1610.2.c.f 12
1610.2.c.g 12
1610.2.c.h 12
1610.2.e $$\chi_{1610}(1289, \cdot)$$ 1610.2.e.a 10 1
1610.2.e.b 14
1610.2.e.c 18
1610.2.e.d 22
1610.2.g $$\chi_{1610}(1609, \cdot)$$ 1610.2.g.a 96 1
1610.2.i $$\chi_{1610}(921, \cdot)$$ n/a 112 2
1610.2.k $$\chi_{1610}(183, \cdot)$$ n/a 144 2
1610.2.m $$\chi_{1610}(783, \cdot)$$ n/a 176 2
1610.2.o $$\chi_{1610}(229, \cdot)$$ n/a 192 2
1610.2.q $$\chi_{1610}(599, \cdot)$$ n/a 176 2
1610.2.s $$\chi_{1610}(551, \cdot)$$ n/a 128 2
1610.2.u $$\chi_{1610}(71, \cdot)$$ n/a 480 10
1610.2.v $$\chi_{1610}(47, \cdot)$$ n/a 352 4
1610.2.x $$\chi_{1610}(137, \cdot)$$ n/a 384 4
1610.2.ba $$\chi_{1610}(419, \cdot)$$ n/a 960 10
1610.2.bc $$\chi_{1610}(29, \cdot)$$ n/a 720 10
1610.2.be $$\chi_{1610}(111, \cdot)$$ n/a 640 10
1610.2.bg $$\chi_{1610}(81, \cdot)$$ n/a 1280 20
1610.2.bh $$\chi_{1610}(13, \cdot)$$ n/a 1920 20
1610.2.bj $$\chi_{1610}(43, \cdot)$$ n/a 1440 20
1610.2.bm $$\chi_{1610}(61, \cdot)$$ n/a 1280 20
1610.2.bo $$\chi_{1610}(9, \cdot)$$ n/a 1920 20
1610.2.bq $$\chi_{1610}(19, \cdot)$$ n/a 1920 20
1610.2.bt $$\chi_{1610}(37, \cdot)$$ n/a 3840 40
1610.2.bv $$\chi_{1610}(3, \cdot)$$ n/a 3840 40

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1610))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1610)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(805))$$$$^{\oplus 2}$$