Defining parameters
| Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8036.bv (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 41 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Sturm bound: | \(2352\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8036, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9600 | 1144 | 8456 |
| Cusp forms | 9216 | 1144 | 8072 |
| Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{new}}(8036, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8036, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8036, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1148, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2009, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4018, [\chi])\)\(^{\oplus 2}\)