Defining parameters
| Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
| Weight: | \( k \) | \(=\) | \( 12 \) |
| Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(384\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(256, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1440 | 360 | 1080 |
| Cusp forms | 1376 | 344 | 1032 |
| Eisenstein series | 64 | 16 | 48 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(256, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{12}^{\mathrm{old}}(256, [\chi])\) into lower level spaces
\( S_{12}^{\mathrm{old}}(256, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)