Defining parameters
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.bz (of order \(42\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 441 \) |
Character field: | \(\Q(\zeta_{42})\) | ||
Sturm bound: | \(672\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6120 | 2040 | 4080 |
Cusp forms | 5976 | 1992 | 3984 |
Eisenstein series | 144 | 48 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)