Defining parameters
| Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 5 \) |
| Character orbit: | \([\chi]\) | \(=\) | 704.t (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 88 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Sturm bound: | \(480\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(704, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1584 | 384 | 1200 |
| Cusp forms | 1488 | 384 | 1104 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(704, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{5}^{\mathrm{old}}(704, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)