Defining parameters
| Level: | \( N \) | \(=\) | \( 6336 = 2^{6} \cdot 3^{2} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6336.ek (of order \(40\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 352 \) |
| Character field: | \(\Q(\zeta_{40})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2304\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6336, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 18688 | 0 | 18688 |
| Cusp forms | 18176 | 0 | 18176 |
| Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{old}}(6336, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3168, [\chi])\)\(^{\oplus 2}\)