Defining parameters
| Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1728.bp (of order \(24\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 288 \) |
| Character field: | \(\Q(\zeta_{24})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(864\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1728, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4704 | 0 | 4704 |
| Cusp forms | 4512 | 0 | 4512 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{3}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)