Defining parameters
| Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 864.j (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(432\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(864, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 600 | 0 | 600 |
| Cusp forms | 552 | 0 | 552 |
| Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{3}^{\mathrm{old}}(864, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)