Defining parameters
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(264\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1089, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 288 | 236 | 52 |
Cusp forms | 240 | 200 | 40 |
Eisenstein series | 48 | 36 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)