Defining parameters
| Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 784.bf (of order \(14\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 392 \) |
| Character field: | \(\Q(\zeta_{14})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(448\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2040 | 0 | 2040 |
| Cusp forms | 1992 | 0 | 1992 |
| Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{4}^{\mathrm{old}}(784, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)