Defining parameters
| Level: | \( N \) | \(=\) | \( 1275 = 3 \cdot 5^{2} \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1275.j (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(720\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1275, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1104 | 344 | 760 |
| Cusp forms | 1056 | 344 | 712 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1275, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1275, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1275, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 2}\)