Defining parameters
| Level: | \( N \) | \(=\) | \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5400.df (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Sturm bound: | \(2160\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8736 | 3840 | 4896 |
| Cusp forms | 8544 | 3840 | 4704 |
| Eisenstein series | 192 | 0 | 192 |
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
\( S_{2}^{\mathrm{old}}(5400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)