Defining parameters
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.v (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(576, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2720 | 0 | 2720 |
Cusp forms | 2656 | 0 | 2656 |
Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{8}^{\mathrm{old}}(576, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)