Defining parameters
| Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 600.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(960\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 864 | 0 | 864 |
| Cusp forms | 816 | 0 | 816 |
| Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{8}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)