Defining parameters
| Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1728.l (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(1152\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1728, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1776 | 192 | 1584 |
| Cusp forms | 1680 | 192 | 1488 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)