Defining parameters
| Level: | \( N \) | = | \( 576 = 2^{6} \cdot 3^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 5 \) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(18432\) | ||
| Trace bound: | \(25\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(576))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 620 | 112 | 508 |
| Cusp forms | 44 | 13 | 31 |
| Eisenstein series | 576 | 99 | 477 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 9 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(576))\)
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 available newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 576.1.b | \(\chi_{576}(415, \cdot)\) | 576.1.b.a | 2 | 1 |
| 576.1.e | \(\chi_{576}(449, \cdot)\) | 576.1.e.a | 2 | 1 |
| 576.1.g | \(\chi_{576}(127, \cdot)\) | 576.1.g.a | 1 | 1 |
| 576.1.h | \(\chi_{576}(161, \cdot)\) | None | 0 | 1 |
| 576.1.j | \(\chi_{576}(17, \cdot)\) | None | 0 | 2 |
| 576.1.m | \(\chi_{576}(271, \cdot)\) | None | 0 | 2 |
| 576.1.n | \(\chi_{576}(353, \cdot)\) | 576.1.n.a | 4 | 2 |
| 576.1.o | \(\chi_{576}(319, \cdot)\) | 576.1.o.a | 4 | 2 |
| 576.1.q | \(\chi_{576}(65, \cdot)\) | None | 0 | 2 |
| 576.1.t | \(\chi_{576}(31, \cdot)\) | None | 0 | 2 |
| 576.1.u | \(\chi_{576}(55, \cdot)\) | None | 0 | 4 |
| 576.1.x | \(\chi_{576}(89, \cdot)\) | None | 0 | 4 |
| 576.1.z | \(\chi_{576}(79, \cdot)\) | None | 0 | 4 |
| 576.1.ba | \(\chi_{576}(113, \cdot)\) | None | 0 | 4 |
| 576.1.bc | \(\chi_{576}(53, \cdot)\) | None | 0 | 8 |
| 576.1.bf | \(\chi_{576}(19, \cdot)\) | None | 0 | 8 |
| 576.1.bh | \(\chi_{576}(7, \cdot)\) | None | 0 | 8 |
| 576.1.bi | \(\chi_{576}(41, \cdot)\) | None | 0 | 8 |
| 576.1.bk | \(\chi_{576}(43, \cdot)\) | None | 0 | 16 |
| 576.1.bn | \(\chi_{576}(5, \cdot)\) | None | 0 | 16 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(576))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(576)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 21}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)