Defining parameters
| Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 588.k (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(672\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(588, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1168 | 134 | 1034 |
| Cusp forms | 1072 | 134 | 938 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(588, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{6}^{\mathrm{old}}(588, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)