Defining parameters
Level: | \( N \) | \(=\) | \( 2000 = 2^{4} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2000.w (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(600\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2000, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1280 | 0 | 1280 |
Cusp forms | 1120 | 0 | 1120 |
Eisenstein series | 160 | 0 | 160 |
Decomposition of \(S_{2}^{\mathrm{old}}(2000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 2}\)