Defining parameters
| Level: | \( N \) | \(=\) | \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5400.z (of order \(5\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
| Character field: | \(\Q(\zeta_{5})\) | ||
| Sturm bound: | \(2160\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4416 | 480 | 3936 |
| Cusp forms | 4224 | 480 | 3744 |
| 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
\( S_{2}^{\mathrm{old}}(5400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)