Defining parameters
| Level: | \( N \) | \(=\) | \( 6000 = 2^{4} \cdot 3 \cdot 5^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6000.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2400\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1240 | 0 | 1240 |
| Cusp forms | 1160 | 0 | 1160 |
| Eisenstein series | 80 | 0 | 80 |
Decomposition of \(S_{2}^{\mathrm{old}}(6000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3000, [\chi])\)\(^{\oplus 2}\)