Defining parameters
| Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1536.z (of order \(64\) and degree \(32\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 256 \) |
| Character field: | \(\Q(\zeta_{64})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(512\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1536, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8320 | 0 | 8320 |
| Cusp forms | 8064 | 0 | 8064 |
| Eisenstein series | 256 | 0 | 256 |
Decomposition of \(S_{2}^{\mathrm{old}}(1536, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1536, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)