Defining parameters
| Level: | \( N \) | \(=\) | \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8040.fx (of order \(66\) and degree \(20\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 335 \) |
| Character field: | \(\Q(\zeta_{66})\) | ||
| Sturm bound: | \(3264\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8040, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 32960 | 4080 | 28880 |
| Cusp forms | 32320 | 4080 | 28240 |
| Eisenstein series | 640 | 0 | 640 |
Decomposition of \(S_{2}^{\mathrm{new}}(8040, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8040, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1340, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2010, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4020, [\chi])\)\(^{\oplus 2}\)