Defining parameters
Level: | \( N \) | \(=\) | \( 4000 = 2^{5} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 4000.cl (of order \(50\) and degree \(20\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 500 \) |
Character field: | \(\Q(\zeta_{50})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(600\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 0 | 240 |
Cusp forms | 80 | 0 | 80 |
Eisenstein series | 160 | 0 | 160 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 0 | 0 | 0 |
Decomposition of \(S_{1}^{\mathrm{old}}(4000, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 4}\)