## Defining parameters

 Level: $$N$$ = $$430 = 2 \cdot 5 \cdot 43$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$33$$ Sturm bound: $$22176$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(430))$$.

Total New Old
Modular forms 5880 1695 4185
Cusp forms 5209 1695 3514
Eisenstein series 671 0 671

## Trace form

 $$1695q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + O(q^{10})$$ $$1695q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + q^{10} + 12q^{11} + 4q^{12} + 14q^{13} + 8q^{14} + 4q^{15} + q^{16} + 18q^{17} + 13q^{18} + 20q^{19} + q^{20} + 32q^{21} + 12q^{22} + 24q^{23} + 4q^{24} + q^{25} + 14q^{26} + 40q^{27} + 8q^{28} + 30q^{29} + 4q^{30} + 4q^{31} + q^{32} - 120q^{33} - 108q^{34} - 76q^{35} - 99q^{36} - 130q^{37} - 148q^{38} - 140q^{39} + q^{40} - 42q^{41} - 136q^{42} - 377q^{43} - 72q^{44} - 197q^{45} - 144q^{46} - 36q^{47} + 4q^{48} - 139q^{49} - 83q^{50} - 96q^{51} - 98q^{52} - 114q^{53} - 86q^{54} - 72q^{55} + 8q^{56} + 52q^{57} + 30q^{58} + 60q^{59} + 4q^{60} + 62q^{61} + 32q^{62} + 104q^{63} + q^{64} + 14q^{65} + 48q^{66} + 68q^{67} + 18q^{68} + 12q^{69} + 8q^{70} - 12q^{71} + 13q^{72} - 10q^{73} + 38q^{74} - 38q^{75} + 20q^{76} - 156q^{77} + 56q^{78} - 88q^{79} + q^{80} - 215q^{81} + 42q^{82} - 84q^{83} + 32q^{84} - 66q^{85} + 43q^{86} - 300q^{87} + 12q^{88} - 78q^{89} + 13q^{90} - 56q^{91} + 24q^{92} - 208q^{93} + 48q^{94} - 64q^{95} + 4q^{96} - 154q^{97} + 57q^{98} - 138q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(430))$$

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
430.2.a $$\chi_{430}(1, \cdot)$$ 430.2.a.a 1 1
430.2.a.b 1
430.2.a.c 1
430.2.a.d 1
430.2.a.e 2
430.2.a.f 2
430.2.a.g 2
430.2.a.h 3
430.2.b $$\chi_{430}(259, \cdot)$$ 430.2.b.a 6 1
430.2.b.b 16
430.2.e $$\chi_{430}(221, \cdot)$$ 430.2.e.a 2 2
430.2.e.b 2
430.2.e.c 2
430.2.e.d 4
430.2.e.e 6
430.2.e.f 6
430.2.e.g 10
430.2.g $$\chi_{430}(257, \cdot)$$ 430.2.g.a 4 2
430.2.g.b 40
430.2.j $$\chi_{430}(49, \cdot)$$ 430.2.j.a 44 2
430.2.k $$\chi_{430}(11, \cdot)$$ 430.2.k.a 12 6
430.2.k.b 18
430.2.k.c 18
430.2.k.d 24
430.2.l $$\chi_{430}(7, \cdot)$$ 430.2.l.a 88 4
430.2.p $$\chi_{430}(59, \cdot)$$ 430.2.p.a 132 6
430.2.q $$\chi_{430}(31, \cdot)$$ 430.2.q.a 36 12
430.2.q.b 48
430.2.q.c 48
430.2.q.d 60
430.2.r $$\chi_{430}(27, \cdot)$$ 430.2.r.a 264 12
430.2.t $$\chi_{430}(9, \cdot)$$ 430.2.t.a 264 12
430.2.x $$\chi_{430}(3, \cdot)$$ 430.2.x.a 528 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(430))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(430)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(86))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(215))$$$$^{\oplus 2}$$