Defining parameters
| Level: | \( N \) | \(=\) | \( 656 = 2^{4} \cdot 41 \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 656.by (of order \(40\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 164 \) |
| Character field: | \(\Q(\zeta_{40})\) | ||
| Sturm bound: | \(504\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(656, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 6816 | 1680 | 5136 |
| Cusp forms | 6624 | 1680 | 4944 |
| Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(656, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{6}^{\mathrm{old}}(656, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(656, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 2}\)