Defining parameters
| Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 22 \) |
| Character orbit: | \([\chi]\) | \(=\) | 75.e (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(220\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(75, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 432 | 256 | 176 |
| Cusp forms | 408 | 248 | 160 |
| Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(75, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{22}^{\mathrm{old}}(75, [\chi])\) into lower level spaces
\( S_{22}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{22}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)