Defining parameters
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.y (of order \(21\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
Character field: | \(\Q(\zeta_{21})\) | ||
Sturm bound: | \(448\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(588, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4104 | 336 | 3768 |
Cusp forms | 3960 | 336 | 3624 |
Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(588, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(588, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)