Defining parameters
| Level: | \( N \) | = | \( 75 = 3 \cdot 5^{2} \) |
| Weight: | \( k \) | = | \( 13 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Sturm bound: | \(5200\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(75))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2456 | 1681 | 775 |
| Cusp forms | 2344 | 1639 | 705 |
| Eisenstein series | 112 | 42 | 70 |
Trace form
Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(75))\)
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 |
|---|---|---|---|---|
| 75.13.c | \(\chi_{75}(26, \cdot)\) | 75.13.c.a | 1 | 1 |
| 75.13.c.b | 2 | |||
| 75.13.c.c | 2 | |||
| 75.13.c.d | 16 | |||
| 75.13.c.e | 16 | |||
| 75.13.c.f | 16 | |||
| 75.13.c.g | 20 | |||
| 75.13.d | \(\chi_{75}(74, \cdot)\) | 75.13.d.a | 2 | 1 |
| 75.13.d.b | 4 | |||
| 75.13.d.c | 32 | |||
| 75.13.d.d | 32 | |||
| 75.13.f | \(\chi_{75}(7, \cdot)\) | 75.13.f.a | 16 | 2 |
| 75.13.f.b | 16 | |||
| 75.13.f.c | 16 | |||
| 75.13.f.d | 24 | |||
| 75.13.h | \(\chi_{75}(14, \cdot)\) | n/a | 472 | 4 |
| 75.13.j | \(\chi_{75}(11, \cdot)\) | n/a | 472 | 4 |
| 75.13.k | \(\chi_{75}(13, \cdot)\) | n/a | 480 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces
\( S_{13}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)