Defining parameters
| Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 414.j (of order \(22\) and degree \(10\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 69 \) |
| Character field: | \(\Q(\zeta_{22})\) | ||
| Sturm bound: | \(288\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(414, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2240 | 240 | 2000 |
| Cusp forms | 2080 | 240 | 1840 |
| Eisenstein series | 160 | 0 | 160 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(414, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(414, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)