Defining parameters
| Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1536.k (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(512\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1536, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 576 | 128 | 448 |
| Cusp forms | 448 | 128 | 320 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1536, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1536, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1536, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)