Defining parameters
| Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1350.bd (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 225 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(540\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4512 | 480 | 4032 |
| Cusp forms | 4128 | 480 | 3648 |
| Eisenstein series | 384 | 0 | 384 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1350, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)