Defining parameters
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.eg (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Sturm bound: | \(768\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1680, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 816 | 200 | 616 |
Cusp forms | 720 | 184 | 536 |
Eisenstein series | 96 | 16 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1680, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)