Defining parameters
| Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4009.bt (of order \(21\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 211 \) |
| Character field: | \(\Q(\zeta_{21})\) | ||
| Sturm bound: | \(706\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4009, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4272 | 3816 | 456 |
| Cusp forms | 4224 | 3816 | 408 |
| Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{2}^{\mathrm{new}}(4009, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4009, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(211, [\chi])\)\(^{\oplus 2}\)