Defining parameters
| Level: | \( N \) | = | \( 75 = 3 \cdot 5^{2} \) |
| Weight: | \( k \) | = | \( 22 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Sturm bound: | \(8800\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(75))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4256 | 2922 | 1334 |
| Cusp forms | 4144 | 2882 | 1262 |
| Eisenstein series | 112 | 40 | 72 |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(75))\)
We only show spaces with even 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 |
|---|---|---|---|---|
| 75.22.a | \(\chi_{75}(1, \cdot)\) | 75.22.a.a | 1 | 1 |
| 75.22.a.b | 1 | |||
| 75.22.a.c | 1 | |||
| 75.22.a.d | 2 | |||
| 75.22.a.e | 3 | |||
| 75.22.a.f | 3 | |||
| 75.22.a.g | 3 | |||
| 75.22.a.h | 4 | |||
| 75.22.a.i | 6 | |||
| 75.22.a.j | 6 | |||
| 75.22.a.k | 8 | |||
| 75.22.a.l | 8 | |||
| 75.22.a.m | 10 | |||
| 75.22.a.n | 10 | |||
| 75.22.b | \(\chi_{75}(49, \cdot)\) | 75.22.b.a | 2 | 1 |
| 75.22.b.b | 2 | |||
| 75.22.b.c | 2 | |||
| 75.22.b.d | 4 | |||
| 75.22.b.e | 6 | |||
| 75.22.b.f | 6 | |||
| 75.22.b.g | 6 | |||
| 75.22.b.h | 8 | |||
| 75.22.b.i | 12 | |||
| 75.22.b.j | 16 | |||
| 75.22.e | \(\chi_{75}(32, \cdot)\) | n/a | 248 | 2 |
| 75.22.g | \(\chi_{75}(16, \cdot)\) | n/a | 424 | 4 |
| 75.22.i | \(\chi_{75}(4, \cdot)\) | n/a | 416 | 4 |
| 75.22.l | \(\chi_{75}(2, \cdot)\) | n/a | 1664 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)