## Defining parameters

 Level: $$N$$ = $$432 = 2^{4} \cdot 3^{3}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$43$$ Sturm bound: $$20736$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(432))$$.

Total New Old
Modular forms 5604 2376 3228
Cusp forms 4765 2232 2533
Eisenstein series 839 144 695

## Trace form

 $$2232q - 16q^{2} - 18q^{3} - 28q^{4} - 21q^{5} - 24q^{6} - 23q^{7} - 16q^{8} - 6q^{9} + O(q^{10})$$ $$2232q - 16q^{2} - 18q^{3} - 28q^{4} - 21q^{5} - 24q^{6} - 23q^{7} - 16q^{8} - 6q^{9} - 28q^{10} - 17q^{11} - 24q^{12} - 39q^{13} - 8q^{14} - 18q^{15} - 20q^{16} - 27q^{17} - 24q^{18} - 19q^{19} + 12q^{20} - 30q^{21} - 4q^{22} - q^{23} - 24q^{24} + 14q^{25} + 16q^{26} - 40q^{28} + 35q^{29} - 24q^{30} + 5q^{31} + 4q^{32} - 30q^{33} - 20q^{34} + 73q^{35} - 24q^{36} + q^{37} - 44q^{38} + 18q^{39} - 60q^{40} + 39q^{41} - 24q^{42} + 41q^{43} - 60q^{44} - 6q^{45} - 76q^{46} + 59q^{47} - 24q^{48} - 64q^{49} - 60q^{50} - 27q^{51} - 60q^{52} - 24q^{53} - 24q^{54} - 30q^{55} - 196q^{56} - 21q^{57} - 124q^{58} - 29q^{59} - 144q^{60} - 103q^{61} - 256q^{62} - 48q^{63} - 100q^{64} - 223q^{65} - 204q^{66} - 67q^{67} - 292q^{68} - 126q^{69} - 220q^{70} - 131q^{71} - 192q^{72} - 71q^{73} - 296q^{74} - 60q^{75} - 220q^{76} - 183q^{77} - 180q^{78} - 79q^{79} - 348q^{80} - 150q^{81} - 176q^{82} - 109q^{83} - 156q^{84} - 81q^{85} - 268q^{86} - 36q^{87} - 132q^{88} - 63q^{89} - 132q^{90} - 81q^{91} - 76q^{92} - 102q^{93} - 60q^{94} - 173q^{95} - 24q^{96} - 39q^{97} - 64q^{98} - 126q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(432))$$

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
432.2.a $$\chi_{432}(1, \cdot)$$ 432.2.a.a 1 1
432.2.a.b 1
432.2.a.c 1
432.2.a.d 1
432.2.a.e 1
432.2.a.f 1
432.2.a.g 1
432.2.a.h 1
432.2.c $$\chi_{432}(431, \cdot)$$ 432.2.c.a 2 1
432.2.c.b 2
432.2.c.c 4
432.2.d $$\chi_{432}(217, \cdot)$$ None 0 1
432.2.f $$\chi_{432}(215, \cdot)$$ None 0 1
432.2.i $$\chi_{432}(145, \cdot)$$ 432.2.i.a 2 2
432.2.i.b 2
432.2.i.c 2
432.2.i.d 4
432.2.k $$\chi_{432}(109, \cdot)$$ 432.2.k.a 4 2
432.2.k.b 4
432.2.k.c 24
432.2.k.d 32
432.2.l $$\chi_{432}(107, \cdot)$$ 432.2.l.a 32 2
432.2.l.b 32
432.2.p $$\chi_{432}(71, \cdot)$$ None 0 2
432.2.r $$\chi_{432}(73, \cdot)$$ None 0 2
432.2.s $$\chi_{432}(143, \cdot)$$ 432.2.s.a 2 2
432.2.s.b 2
432.2.s.c 2
432.2.s.d 2
432.2.s.e 4
432.2.u $$\chi_{432}(49, \cdot)$$ 432.2.u.a 6 6
432.2.u.b 12
432.2.u.c 12
432.2.u.d 18
432.2.u.e 24
432.2.u.f 30
432.2.v $$\chi_{432}(35, \cdot)$$ 432.2.v.a 88 4
432.2.y $$\chi_{432}(37, \cdot)$$ 432.2.y.a 4 4
432.2.y.b 4
432.2.y.c 4
432.2.y.d 4
432.2.y.e 72
432.2.bb $$\chi_{432}(25, \cdot)$$ None 0 6
432.2.bd $$\chi_{432}(23, \cdot)$$ None 0 6
432.2.be $$\chi_{432}(47, \cdot)$$ 432.2.be.a 36 6
432.2.be.b 36
432.2.be.c 36
432.2.bg $$\chi_{432}(13, \cdot)$$ 432.2.bg.a 840 12
432.2.bj $$\chi_{432}(11, \cdot)$$ 432.2.bj.a 840 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(432))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(432)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 2}$$