Defining parameters
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 172 \) |
Character field: | \(\Q\) | ||
Sturm bound: | \(528\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(688, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 446 | 110 | 336 |
Cusp forms | 434 | 110 | 324 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(688, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{6}^{\mathrm{old}}(688, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(688, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(172, [\chi])\)\(^{\oplus 3}\)