Defining parameters
| Level: | \( N \) | \(=\) | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 312.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(224\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(312, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 176 | 0 | 176 |
| Cusp forms | 160 | 0 | 160 |
| Eisenstein series | 16 | 0 | 16 |
Decomposition of \(S_{4}^{\mathrm{old}}(312, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(312, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)