Defining parameters
| Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 5 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1152.j (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(960\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(1152, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1600 | 128 | 1472 |
| Cusp forms | 1472 | 128 | 1344 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{5}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)