Defining parameters
| Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1728.bh (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 216 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Sturm bound: | \(864\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1728, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3528 | 864 | 2664 |
| Cusp forms | 3384 | 864 | 2520 |
| Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)