Defining parameters
| Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1000.w (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(300\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1360 | 0 | 1360 |
| Cusp forms | 1040 | 0 | 1040 |
| Eisenstein series | 320 | 0 | 320 |
Decomposition of \(S_{2}^{\mathrm{old}}(1000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)