Defining parameters
| Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4010.bf (of order \(40\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 401 \) |
| Character field: | \(\Q(\zeta_{40})\) | ||
| Sturm bound: | \(1206\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4010, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9728 | 2144 | 7584 |
| Cusp forms | 9600 | 2144 | 7456 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{2}^{\mathrm{new}}(4010, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4010, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4010, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(401, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(802, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2005, [\chi])\)\(^{\oplus 2}\)