Defining parameters
| Level: | \( N \) | \(=\) | \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5400.bp (of order \(9\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
| Character field: | \(\Q(\zeta_{9})\) | ||
| Sturm bound: | \(2160\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 6624 | 1026 | 5598 |
| Cusp forms | 6336 | 1026 | 5310 |
| Eisenstein series | 288 | 0 | 288 |
Decomposition of \(S_{2}^{\mathrm{new}}(5400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(5400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)