Defining parameters
| Level: | \( N \) | = | \( 25 = 5^{2} \) |
| Weight: | \( k \) | = | \( 9 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(450\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(25))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 214 | 194 | 20 |
| Cusp forms | 186 | 174 | 12 |
| Eisenstein series | 28 | 20 | 8 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(25))\)
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 |
|---|---|---|---|---|
| 25.9.c | \(\chi_{25}(7, \cdot)\) | 25.9.c.a | 4 | 2 |
| 25.9.c.b | 6 | |||
| 25.9.c.c | 12 | |||
| 25.9.f | \(\chi_{25}(2, \cdot)\) | 25.9.f.a | 152 | 8 |
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)