Defining parameters
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.dh (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 225 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Sturm bound: | \(1440\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8704 | 2160 | 6544 |
Cusp forms | 8576 | 2160 | 6416 |
Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)