Defining parameters
| Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8008.w (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
| Character field: | \(\Q\) | ||
| Sturm bound: | \(2688\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8008, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1360 | 212 | 1148 |
| Cusp forms | 1328 | 212 | 1116 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{2}^{\mathrm{new}}(8008, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8008, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)