Defining parameters
| Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1176.bv (of order \(14\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 196 \) |
| Character field: | \(\Q(\zeta_{14})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(896\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1176, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4080 | 0 | 4080 |
| Cusp forms | 3984 | 0 | 3984 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{4}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)