Defining parameters
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.u (of order \(7\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 43 \) |
Character field: | \(\Q(\zeta_{7})\) | ||
Sturm bound: | \(528\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(688, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2676 | 666 | 2010 |
Cusp forms | 2604 | 654 | 1950 |
Eisenstein series | 72 | 12 | 60 |
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
\( S_{6}^{\mathrm{old}}(688, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(86, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(172, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(344, [\chi])\)\(^{\oplus 2}\)