Defining parameters
| Level: | \( N \) | \(=\) | \( 6912 = 2^{8} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6912.cp (of order \(96\) and degree \(32\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1152 \) |
| Character field: | \(\Q(\zeta_{96})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2304\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6912, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 37248 | 0 | 37248 |
| Cusp forms | 36480 | 0 | 36480 |
| Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{old}}(6912, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3456, [\chi])\)\(^{\oplus 2}\)