Defining parameters
| Level: | \( N \) | = | \( 2209 = 47^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(406456\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2209))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1658 | 1608 | 50 |
| Cusp forms | 48 | 44 | 4 |
| Eisenstein series | 1610 | 1564 | 46 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 44 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2209))\)
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 |
|---|---|---|---|---|
| 2209.1.b | \(\chi_{2209}(2208, \cdot)\) | None | 0 | 1 |
| 2209.1.d | \(\chi_{2209}(67, \cdot)\) | 2209.1.d.a | 44 | 22 |
| 2209.1.f | \(\chi_{2209}(46, \cdot)\) | None | 0 | 46 |
| 2209.1.h | \(\chi_{2209}(5, \cdot)\) | None | 0 | 1012 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2209))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2209)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 2}\)