Defining parameters
| Level: | \( N \) | = | \( 2916 = 2^{2} \cdot 3^{6} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 15 \) | ||
| Sturm bound: | \(472392\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2916))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3400 | 732 | 2668 |
| Cusp forms | 160 | 84 | 76 |
| Eisenstein series | 3240 | 648 | 2592 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 84 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2916))\)
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 |
|---|---|---|---|---|
| 2916.1.c | \(\chi_{2916}(1457, \cdot)\) | None | 0 | 1 |
| 2916.1.d | \(\chi_{2916}(1459, \cdot)\) | 2916.1.d.a | 3 | 1 |
| 2916.1.d.b | 3 | |||
| 2916.1.f | \(\chi_{2916}(487, \cdot)\) | 2916.1.f.a | 6 | 2 |
| 2916.1.f.b | 6 | |||
| 2916.1.g | \(\chi_{2916}(485, \cdot)\) | None | 0 | 2 |
| 2916.1.j | \(\chi_{2916}(163, \cdot)\) | 2916.1.j.a | 6 | 6 |
| 2916.1.j.b | 6 | |||
| 2916.1.j.c | 6 | |||
| 2916.1.j.d | 6 | |||
| 2916.1.j.e | 6 | |||
| 2916.1.j.f | 6 | |||
| 2916.1.j.g | 6 | |||
| 2916.1.j.h | 6 | |||
| 2916.1.k | \(\chi_{2916}(161, \cdot)\) | 2916.1.k.a | 6 | 6 |
| 2916.1.k.b | 6 | |||
| 2916.1.k.c | 6 | |||
| 2916.1.n | \(\chi_{2916}(55, \cdot)\) | None | 0 | 18 |
| 2916.1.o | \(\chi_{2916}(53, \cdot)\) | None | 0 | 18 |
| 2916.1.r | \(\chi_{2916}(19, \cdot)\) | None | 0 | 54 |
| 2916.1.s | \(\chi_{2916}(17, \cdot)\) | None | 0 | 54 |
| 2916.1.v | \(\chi_{2916}(7, \cdot)\) | None | 0 | 162 |
| 2916.1.w | \(\chi_{2916}(5, \cdot)\) | None | 0 | 162 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2916))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2916)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 21}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(486))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1458))\)\(^{\oplus 2}\)