Defining parameters
| Level: | \( N \) | \(=\) | \( 8304 = 2^{4} \cdot 3 \cdot 173 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8304.cp (of order \(172\) and degree \(84\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1384 \) |
| Character field: | \(\Q(\zeta_{172})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2784\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8304, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 117600 | 0 | 117600 |
| Cusp forms | 116256 | 0 | 116256 |
| Eisenstein series | 1344 | 0 | 1344 |
Decomposition of \(S_{2}^{\mathrm{old}}(8304, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4152, [\chi])\)\(^{\oplus 2}\)