Defining parameters
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.cl (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 180 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1536 | 0 | 1536 |
Cusp forms | 1344 | 0 | 1344 |
Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)