Defining parameters
| Level: | \( N \) | \(=\) | \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6480.ds (of order \(27\) and degree \(18\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 81 \) |
| Character field: | \(\Q(\zeta_{27})\) | ||
| Sturm bound: | \(2592\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6480, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 23544 | 3888 | 19656 |
| Cusp forms | 23112 | 3888 | 19224 |
| Eisenstein series | 432 | 0 | 432 |
Decomposition of \(S_{2}^{\mathrm{new}}(6480, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(6480, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6480, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3240, [\chi])\)\(^{\oplus 2}\)