Defining parameters
| Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1728.bl (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 216 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1728, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1800 | 432 | 1368 |
| Cusp forms | 1656 | 432 | 1224 |
| Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)