## Defining parameters

 Level: $$N$$ = $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$58$$ Sturm bound: $$28224$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(490))$$.

Total New Old
Modular forms 7536 2067 5469
Cusp forms 6577 2067 4510
Eisenstein series 959 0 959

## Trace form

 $$2067q - q^{2} + 4q^{3} + 7q^{4} + 11q^{5} + 20q^{6} + 16q^{7} - q^{8} + 43q^{9} + O(q^{10})$$ $$2067q - q^{2} + 4q^{3} + 7q^{4} + 11q^{5} + 20q^{6} + 16q^{7} - q^{8} + 43q^{9} + 11q^{10} + 36q^{11} + 4q^{12} + 26q^{13} + 12q^{14} + 44q^{15} + 7q^{16} + 78q^{17} + 35q^{18} + 68q^{19} + 11q^{20} + 52q^{21} + 36q^{22} + 72q^{23} + 20q^{24} - 17q^{25} + 10q^{26} - 8q^{27} - 8q^{28} - 30q^{29} - 100q^{30} - 16q^{31} - q^{32} - 96q^{33} - 66q^{34} - 30q^{35} - 53q^{36} - 134q^{37} - 128q^{38} - 236q^{39} - 31q^{40} - 114q^{41} - 180q^{42} - 100q^{43} - 96q^{44} - 211q^{45} - 228q^{46} - 120q^{47} - 24q^{48} - 236q^{49} - 13q^{50} - 168q^{51} - 2q^{52} + 18q^{53} - 148q^{54} - 126q^{55} - 72q^{56} - 40q^{57} - 54q^{58} - 108q^{59} + 2q^{60} - 122q^{61} + 28q^{62} - 24q^{63} + 7q^{64} + 10q^{65} + 144q^{66} - 4q^{67} + 78q^{68} + 96q^{69} + 42q^{70} + 120q^{71} + 35q^{72} + 38q^{73} + 106q^{74} + 52q^{75} + 68q^{76} + 96q^{77} + 136q^{78} + 80q^{79} + 11q^{80} + 7q^{81} + 102q^{82} - 36q^{83} + 52q^{84} + 18q^{85} + 52q^{86} - 120q^{87} - 12q^{88} - 162q^{89} - 49q^{90} - 76q^{91} - 24q^{92} - 424q^{93} - 332q^{95} - 28q^{96} - 202q^{97} - 48q^{98} - 252q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$

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
490.2.a $$\chi_{490}(1, \cdot)$$ 490.2.a.a 1 1
490.2.a.b 1
490.2.a.c 1
490.2.a.d 1
490.2.a.e 1
490.2.a.f 1
490.2.a.g 1
490.2.a.h 1
490.2.a.i 1
490.2.a.j 1
490.2.a.k 1
490.2.a.l 2
490.2.a.m 2
490.2.c $$\chi_{490}(99, \cdot)$$ 490.2.c.a 2 1
490.2.c.b 2
490.2.c.c 2
490.2.c.d 2
490.2.c.e 4
490.2.c.f 4
490.2.c.g 4
490.2.e $$\chi_{490}(361, \cdot)$$ 490.2.e.a 2 2
490.2.e.b 2
490.2.e.c 2
490.2.e.d 2
490.2.e.e 2
490.2.e.f 2
490.2.e.g 2
490.2.e.h 2
490.2.e.i 4
490.2.e.j 4
490.2.g $$\chi_{490}(97, \cdot)$$ 490.2.g.a 8 2
490.2.g.b 16
490.2.g.c 16
490.2.i $$\chi_{490}(79, \cdot)$$ 490.2.i.a 4 2
490.2.i.b 4
490.2.i.c 8
490.2.i.d 8
490.2.i.e 8
490.2.i.f 8
490.2.k $$\chi_{490}(71, \cdot)$$ 490.2.k.a 6 6
490.2.k.b 6
490.2.k.c 6
490.2.k.d 12
490.2.k.e 12
490.2.k.f 24
490.2.k.g 30
490.2.l $$\chi_{490}(117, \cdot)$$ 490.2.l.a 16 4
490.2.l.b 16
490.2.l.c 16
490.2.l.d 32
490.2.p $$\chi_{490}(29, \cdot)$$ 490.2.p.a 168 6
490.2.q $$\chi_{490}(11, \cdot)$$ 490.2.q.a 48 12
490.2.q.b 60
490.2.q.c 60
490.2.q.d 72
490.2.s $$\chi_{490}(13, \cdot)$$ 490.2.s.a 336 12
490.2.t $$\chi_{490}(9, \cdot)$$ 490.2.t.a 336 12
490.2.w $$\chi_{490}(3, \cdot)$$ 490.2.w.a 672 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(490))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(490)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 2}$$