# Properties

 Label 490.2 Level 490 Weight 2 Dimension 2067 Nonzero newspaces 12 Newform subspaces 58 Sturm bound 28224 Trace bound 4

## 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

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

## 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

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