Defining parameters
| Level: | \( N \) | \(=\) | \( 6000 = 2^{4} \cdot 3 \cdot 5^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6000.dc (of order \(25\) and degree \(20\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 125 \) |
| Character field: | \(\Q(\zeta_{25})\) | ||
| Sturm bound: | \(2400\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 24240 | 3000 | 21240 |
| Cusp forms | 23760 | 3000 | 20760 |
| Eisenstein series | 480 | 0 | 480 |
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
\( S_{2}^{\mathrm{old}}(6000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(750, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1500, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3000, [\chi])\)\(^{\oplus 2}\)