Defining parameters
| Level: | \( N \) | = | \( 3645 = 3^{6} \cdot 5 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 8 \) | ||
| Sturm bound: | \(944784\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3645))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5312 | 1992 | 3320 |
| Cusp forms | 128 | 48 | 80 |
| Eisenstein series | 5184 | 1944 | 3240 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 48 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3645))\)
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 |
|---|---|---|---|---|
| 3645.1.c | \(\chi_{3645}(2186, \cdot)\) | None | 0 | 1 |
| 3645.1.d | \(\chi_{3645}(3644, \cdot)\) | None | 0 | 1 |
| 3645.1.g | \(\chi_{3645}(2188, \cdot)\) | None | 0 | 2 |
| 3645.1.h | \(\chi_{3645}(1214, \cdot)\) | None | 0 | 2 |
| 3645.1.i | \(\chi_{3645}(971, \cdot)\) | None | 0 | 2 |
| 3645.1.l | \(\chi_{3645}(487, \cdot)\) | None | 0 | 4 |
| 3645.1.n | \(\chi_{3645}(404, \cdot)\) | 3645.1.n.a | 6 | 6 |
| 3645.1.n.b | 6 | |||
| 3645.1.n.c | 6 | |||
| 3645.1.n.d | 6 | |||
| 3645.1.n.e | 6 | |||
| 3645.1.n.f | 6 | |||
| 3645.1.n.g | 6 | |||
| 3645.1.n.h | 6 | |||
| 3645.1.o | \(\chi_{3645}(161, \cdot)\) | None | 0 | 6 |
| 3645.1.s | \(\chi_{3645}(82, \cdot)\) | None | 0 | 12 |
| 3645.1.u | \(\chi_{3645}(26, \cdot)\) | None | 0 | 18 |
| 3645.1.v | \(\chi_{3645}(134, \cdot)\) | None | 0 | 18 |
| 3645.1.x | \(\chi_{3645}(28, \cdot)\) | None | 0 | 36 |
| 3645.1.z | \(\chi_{3645}(71, \cdot)\) | None | 0 | 54 |
| 3645.1.bb | \(\chi_{3645}(44, \cdot)\) | None | 0 | 54 |
| 3645.1.bd | \(\chi_{3645}(37, \cdot)\) | None | 0 | 108 |
| 3645.1.bf | \(\chi_{3645}(14, \cdot)\) | None | 0 | 162 |
| 3645.1.bg | \(\chi_{3645}(11, \cdot)\) | None | 0 | 162 |
| 3645.1.bi | \(\chi_{3645}(7, \cdot)\) | None | 0 | 324 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3645))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(3645)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1215))\)\(^{\oplus 2}\)