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