Defining parameters
| Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3072.s (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 192 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Sturm bound: | \(1024\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4352 | 1088 | 3264 |
| Cusp forms | 3840 | 960 | 2880 |
| Eisenstein series | 512 | 128 | 384 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)