## Defining parameters

 Level: $$N$$ = $$432 = 2^{4} \cdot 3^{3}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$3$$ Sturm bound: $$10368$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(432))$$.

Total New Old
Modular forms 460 79 381
Cusp forms 40 7 33
Eisenstein series 420 72 348

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 4 0

## Trace form

 $$7 q + q^{7} + O(q^{10})$$ $$7 q + q^{7} - 3 q^{13} - 4 q^{16} + q^{19} - q^{25} + 4 q^{28} + 2 q^{31} - 4 q^{34} - 3 q^{37} - 4 q^{40} - 6 q^{43} - 4 q^{49} + 4 q^{52} - 3 q^{61} + 5 q^{67} + 4 q^{70} + q^{73} + q^{79} - 4 q^{85} + 4 q^{88} - 5 q^{91} + 4 q^{94} + 5 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(432))$$

We only show spaces with odd 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
432.1.b $$\chi_{432}(55, \cdot)$$ None 0 1
432.1.e $$\chi_{432}(161, \cdot)$$ 432.1.e.a 1 1
432.1.g $$\chi_{432}(271, \cdot)$$ 432.1.g.a 2 1
432.1.h $$\chi_{432}(377, \cdot)$$ None 0 1
432.1.j $$\chi_{432}(53, \cdot)$$ 432.1.j.a 4 2
432.1.m $$\chi_{432}(163, \cdot)$$ None 0 2
432.1.n $$\chi_{432}(89, \cdot)$$ None 0 2
432.1.o $$\chi_{432}(127, \cdot)$$ None 0 2
432.1.q $$\chi_{432}(17, \cdot)$$ None 0 2
432.1.t $$\chi_{432}(199, \cdot)$$ None 0 2
432.1.w $$\chi_{432}(19, \cdot)$$ None 0 4
432.1.x $$\chi_{432}(125, \cdot)$$ None 0 4
432.1.z $$\chi_{432}(7, \cdot)$$ None 0 6
432.1.ba $$\chi_{432}(31, \cdot)$$ None 0 6
432.1.bc $$\chi_{432}(65, \cdot)$$ None 0 6
432.1.bf $$\chi_{432}(41, \cdot)$$ None 0 6
432.1.bh $$\chi_{432}(43, \cdot)$$ None 0 12
432.1.bi $$\chi_{432}(5, \cdot)$$ None 0 12

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(432))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(432)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 2}$$