Defining parameters
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.bd (of order \(128\) and degree \(64\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 512 \) |
Character field: | \(\Q(\zeta_{128})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(1024\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 33024 | 0 | 33024 |
Cusp forms | 32512 | 0 | 32512 |
Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)