Defining parameters
| Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 672.cc (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 336 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(512\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(672, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1568 | 0 | 1568 |
| Cusp forms | 1504 | 0 | 1504 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{4}^{\mathrm{old}}(672, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)