Defining parameters
| Level: | \( N \) | = | \( 1215 = 3^{5} \cdot 5 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(104976\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1215))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1550 | 594 | 956 |
| Cusp forms | 38 | 18 | 20 |
| Eisenstein series | 1512 | 576 | 936 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 18 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1215))\)
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 |
|---|---|---|---|---|
| 1215.1.c | \(\chi_{1215}(971, \cdot)\) | None | 0 | 1 |
| 1215.1.d | \(\chi_{1215}(1214, \cdot)\) | 1215.1.d.a | 3 | 1 |
| 1215.1.d.b | 3 | |||
| 1215.1.g | \(\chi_{1215}(487, \cdot)\) | None | 0 | 2 |
| 1215.1.h | \(\chi_{1215}(404, \cdot)\) | 1215.1.h.a | 6 | 2 |
| 1215.1.h.b | 6 | |||
| 1215.1.i | \(\chi_{1215}(161, \cdot)\) | None | 0 | 2 |
| 1215.1.l | \(\chi_{1215}(82, \cdot)\) | None | 0 | 4 |
| 1215.1.n | \(\chi_{1215}(134, \cdot)\) | None | 0 | 6 |
| 1215.1.o | \(\chi_{1215}(26, \cdot)\) | None | 0 | 6 |
| 1215.1.s | \(\chi_{1215}(28, \cdot)\) | None | 0 | 12 |
| 1215.1.u | \(\chi_{1215}(71, \cdot)\) | None | 0 | 18 |
| 1215.1.v | \(\chi_{1215}(44, \cdot)\) | None | 0 | 18 |
| 1215.1.x | \(\chi_{1215}(37, \cdot)\) | None | 0 | 36 |
| 1215.1.z | \(\chi_{1215}(11, \cdot)\) | None | 0 | 54 |
| 1215.1.bb | \(\chi_{1215}(14, \cdot)\) | None | 0 | 54 |
| 1215.1.bc | \(\chi_{1215}(7, \cdot)\) | None | 0 | 108 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1215))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1215)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 2}\)