Defining parameters
| Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 342.u (of order \(9\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
| Character field: | \(\Q(\zeta_{9})\) | ||
| Sturm bound: | \(240\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(342, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1128 | 150 | 978 |
| Cusp forms | 1032 | 150 | 882 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(342, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(342, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)