Defining parameters
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.g (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(64, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 616 | 0 | 616 |
Cusp forms | 600 | 0 | 600 |
Eisenstein series | 16 | 0 | 16 |
Decomposition of \(S_{20}^{\mathrm{old}}(64, [\chi])\) into lower level spaces
\( S_{20}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{20}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)