Defining parameters
| Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 392.m (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(336\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(392, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 576 | 408 | 168 |
| Cusp forms | 544 | 392 | 152 |
| Eisenstein series | 32 | 16 | 16 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(392, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{6}^{\mathrm{old}}(392, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(392, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)