Defining parameters
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.p (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 96 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(192, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1040 | 0 | 1040 |
Cusp forms | 1008 | 0 | 1008 |
Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{9}^{\mathrm{old}}(192, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)