Defining parameters
| Level: | \( N \) | = | \( 9 = 3^{2} \) |
| Weight: | \( k \) | = | \( 7 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(42\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(9))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 22 | 16 | 6 |
| Cusp forms | 14 | 12 | 2 |
| Eisenstein series | 8 | 4 | 4 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)
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 |
|---|---|---|---|---|
| 9.7.b | \(\chi_{9}(8, \cdot)\) | 9.7.b.a | 2 | 1 |
| 9.7.d | \(\chi_{9}(2, \cdot)\) | 9.7.d.a | 10 | 2 |
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)