Defining parameters
| Level: | \( N \) | \(=\) | \( 6000 = 2^{4} \cdot 3 \cdot 5^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6000.cq (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1200 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Sturm bound: | \(2400\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9760 | 5856 | 3904 |
| Cusp forms | 9440 | 5664 | 3776 |
| Eisenstein series | 320 | 192 | 128 |
Decomposition of \(S_{2}^{\mathrm{new}}(6000, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(6000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)