Defining parameters
| Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 9 \) |
| Character orbit: | \([\chi]\) | \(=\) | 252.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 84 \) |
| Character field: | \(\Q\) | ||
| Sturm bound: | \(432\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(252, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 392 | 128 | 264 |
| Cusp forms | 376 | 128 | 248 |
| Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(252, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{9}^{\mathrm{old}}(252, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)