Defining parameters
| Level: | \( N \) | \(=\) | \( 6912 = 2^{8} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6912.s (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(2304\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6912, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2448 | 200 | 2248 |
| Cusp forms | 2160 | 184 | 1976 |
| Eisenstein series | 288 | 16 | 272 |
Decomposition of \(S_{2}^{\mathrm{new}}(6912, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(6912, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 5}\)