Defining parameters
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 21 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 98 | 286 |
Cusp forms | 336 | 92 | 244 |
Eisenstein series | 48 | 6 | 42 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)