Defining parameters
| Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 588.y (of order \(21\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
| Character field: | \(\Q(\zeta_{21})\) | ||
| Sturm bound: | \(896\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(588, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9480 | 780 | 8700 |
| Cusp forms | 9336 | 780 | 8556 |
| Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(588, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{8}^{\mathrm{old}}(588, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)