Defining parameters
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.bi (of order \(36\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 432 \) |
Character field: | \(\Q(\zeta_{36})\) | ||
Sturm bound: | \(648\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1296, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5256 | 1752 | 3504 |
Cusp forms | 5112 | 1704 | 3408 |
Eisenstein series | 144 | 48 | 96 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)