## Defining parameters

 Level: $$N$$ = $$290 = 2 \cdot 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$37$$ Sturm bound: $$10080$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(290))$$.

Total New Old
Modular forms 2744 771 1973
Cusp forms 2297 771 1526
Eisenstein series 447 0 447

## Trace form

 $$771 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10})$$ $$771 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + q^{10} + 12 q^{11} + 4 q^{12} + 14 q^{13} + 8 q^{14} + 4 q^{15} + q^{16} + 18 q^{17} + 13 q^{18} + 20 q^{19} - 6 q^{20} - 80 q^{21} - 44 q^{22} - 32 q^{23} - 52 q^{24} - 55 q^{25} - 56 q^{26} - 128 q^{27} + 8 q^{28} - 83 q^{29} - 80 q^{30} - 80 q^{31} + q^{32} - 120 q^{33} - 52 q^{34} - 48 q^{35} - 43 q^{36} - 18 q^{37} - 36 q^{38} - 56 q^{39} - 6 q^{40} + 42 q^{41} + 32 q^{42} + 44 q^{43} + 12 q^{44} - 22 q^{45} + 24 q^{46} - 8 q^{47} + 4 q^{48} - 55 q^{49} + q^{50} - 40 q^{51} + 14 q^{52} - 72 q^{53} + 40 q^{54} - 100 q^{55} + 8 q^{56} - 32 q^{57} + 29 q^{58} + 4 q^{59} + 4 q^{60} - 50 q^{61} + 32 q^{62} - 120 q^{63} + q^{64} - 49 q^{65} + 48 q^{66} - 44 q^{67} + 18 q^{68} - 16 q^{69} - 20 q^{70} - 152 q^{71} + 13 q^{72} - 108 q^{73} - 130 q^{74} - 136 q^{75} - 92 q^{76} - 184 q^{77} - 168 q^{78} - 32 q^{79} + q^{80} - 327 q^{81} - 70 q^{82} - 140 q^{83} - 136 q^{84} - 150 q^{85} - 236 q^{86} - 164 q^{87} + 12 q^{88} - 190 q^{89} - 127 q^{90} - 224 q^{91} - 144 q^{92} - 96 q^{93} - 64 q^{94} - 204 q^{95} + 4 q^{96} - 28 q^{97} - 167 q^{98} - 236 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(290))$$

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
290.2.a $$\chi_{290}(1, \cdot)$$ 290.2.a.a 1 1
290.2.a.b 2
290.2.a.c 2
290.2.a.d 3
290.2.a.e 3
290.2.b $$\chi_{290}(59, \cdot)$$ 290.2.b.a 4 1
290.2.b.b 10
290.2.c $$\chi_{290}(231, \cdot)$$ 290.2.c.a 2 1
290.2.c.b 4
290.2.c.c 4
290.2.d $$\chi_{290}(289, \cdot)$$ 290.2.d.a 8 1
290.2.d.b 8
290.2.e $$\chi_{290}(17, \cdot)$$ 290.2.e.a 2 2
290.2.e.b 2
290.2.e.c 2
290.2.e.d 4
290.2.e.e 8
290.2.e.f 12
290.2.j $$\chi_{290}(133, \cdot)$$ 290.2.j.a 2 2
290.2.j.b 2
290.2.j.c 2
290.2.j.d 4
290.2.j.e 8
290.2.j.f 12
290.2.k $$\chi_{290}(81, \cdot)$$ 290.2.k.a 12 6
290.2.k.b 12
290.2.k.c 18
290.2.k.d 18
290.2.l $$\chi_{290}(9, \cdot)$$ 290.2.l.a 48 6
290.2.l.b 48
290.2.m $$\chi_{290}(51, \cdot)$$ 290.2.m.a 24 6
290.2.m.b 36
290.2.n $$\chi_{290}(49, \cdot)$$ 290.2.n.a 84 6
290.2.o $$\chi_{290}(3, \cdot)$$ 290.2.o.a 84 12
290.2.o.b 96
290.2.t $$\chi_{290}(73, \cdot)$$ 290.2.t.a 84 12
290.2.t.b 96

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(290))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(290)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 2}$$