## Defining parameters

 Level: $$N$$ = $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$15$$ Sturm bound: $$6336$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(230))$$.

Total New Old
Modular forms 1760 485 1275
Cusp forms 1409 485 924
Eisenstein series 351 0 351

## Trace form

 $$485 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10})$$ $$485 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + q^{10} + 12 q^{11} + 4 q^{12} + 14 q^{13} + 8 q^{14} - 18 q^{15} + q^{16} - 26 q^{17} - 75 q^{18} - 24 q^{19} - 21 q^{20} - 100 q^{21} - 32 q^{22} - 65 q^{23} + 4 q^{24} - 43 q^{25} - 30 q^{26} - 92 q^{27} - 36 q^{28} - 14 q^{29} - 40 q^{30} - 12 q^{31} + q^{32} + 4 q^{33} + 18 q^{34} - 14 q^{35} + 13 q^{36} - 50 q^{37} + 20 q^{38} - 32 q^{39} + q^{40} - 2 q^{41} + 32 q^{42} - 44 q^{43} + 12 q^{44} - 53 q^{45} + 23 q^{46} - 40 q^{47} + 4 q^{48} - 75 q^{49} + q^{50} - 16 q^{51} + 14 q^{52} + 10 q^{53} - 4 q^{54} - 76 q^{55} - 36 q^{56} - 140 q^{57} - 58 q^{58} - 160 q^{59} - 18 q^{60} - 114 q^{61} - 100 q^{62} - 116 q^{63} + q^{64} - 140 q^{65} - 128 q^{66} - 20 q^{67} - 70 q^{68} - 128 q^{69} - 80 q^{70} - 148 q^{71} - 75 q^{72} - 14 q^{73} - 138 q^{74} - 172 q^{75} + 20 q^{76} - 124 q^{77} - 76 q^{78} - 140 q^{79} - 21 q^{80} - 143 q^{81} - 46 q^{82} - 92 q^{83} - 12 q^{84} - 48 q^{85} - 12 q^{87} + 12 q^{88} + 46 q^{89} + 13 q^{90} + 24 q^{91} + 23 q^{92} + 128 q^{93} + 48 q^{94} + 42 q^{95} + 4 q^{96} + 186 q^{97} + 145 q^{98} + 244 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$

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
230.2.a $$\chi_{230}(1, \cdot)$$ 230.2.a.a 2 1
230.2.a.b 2
230.2.a.c 2
230.2.a.d 3
230.2.b $$\chi_{230}(139, \cdot)$$ 230.2.b.a 4 1
230.2.b.b 8
230.2.e $$\chi_{230}(137, \cdot)$$ 230.2.e.a 8 2
230.2.e.b 8
230.2.e.c 8
230.2.g $$\chi_{230}(31, \cdot)$$ 230.2.g.a 10 10
230.2.g.b 20
230.2.g.c 20
230.2.g.d 30
230.2.j $$\chi_{230}(9, \cdot)$$ 230.2.j.a 120 10
230.2.l $$\chi_{230}(7, \cdot)$$ 230.2.l.a 240 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(230))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(230)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 2}$$