Defining parameters
| Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 360.bi (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(432\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(360, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 736 | 180 | 556 |
| Cusp forms | 704 | 180 | 524 |
| Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(360, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{6}^{\mathrm{old}}(360, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)