Defining parameters
| Level: | \( N \) | = | \( 22 = 2 \cdot 11 \) |
| Weight: | \( k \) | = | \( 3 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(90\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(22))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 40 | 10 | 30 |
| Cusp forms | 20 | 10 | 10 |
| Eisenstein series | 20 | 0 | 20 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)
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 |
|---|---|---|---|---|
| 22.3.b | \(\chi_{22}(21, \cdot)\) | 22.3.b.a | 2 | 1 |
| 22.3.d | \(\chi_{22}(7, \cdot)\) | 22.3.d.a | 8 | 4 |
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)