Defining parameters
| Level: | \( N \) | \(=\) | \( 42237 = 3^{2} \cdot 13 \cdot 19^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 42237.gt (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2223 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(10640\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(42237, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 21440 | 19168 | 2272 |
| Cusp forms | 21120 | 18912 | 2208 |
| Eisenstein series | 320 | 256 | 64 |
Decomposition of \(S_{2}^{\mathrm{new}}(42237, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(42237, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(42237, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(2223, [\chi])\)\(^{\oplus 2}\)