Defining parameters
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.bd (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 216 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1296, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3960 | 0 | 3960 |
Cusp forms | 3816 | 0 | 3816 |
Eisenstein series | 144 | 0 | 144 |
Decomposition of \(S_{4}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)