Defining parameters
| Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 392.bb (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 196 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(168\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(392, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1392 | 0 | 1392 |
| Cusp forms | 1296 | 0 | 1296 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{3}^{\mathrm{old}}(392, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(392, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)