Defining parameters
| Level: | \( N \) | = | \( 18 = 2 \cdot 3^{2} \) |
| Weight: | \( k \) | = | \( 9 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(162\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(18))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 80 | 20 | 60 |
| Cusp forms | 64 | 20 | 44 |
| Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(18))\)
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 |
|---|---|---|---|---|
| 18.9.b | \(\chi_{18}(17, \cdot)\) | 18.9.b.a | 2 | 1 |
| 18.9.b.b | 2 | |||
| 18.9.d | \(\chi_{18}(5, \cdot)\) | 18.9.d.a | 16 | 2 |
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)