Defining parameters
| Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8004.cp (of order \(44\) and degree \(20\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 667 \) |
| Character field: | \(\Q(\zeta_{44})\) | ||
| Sturm bound: | \(2880\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8004, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 29040 | 2400 | 26640 |
| Cusp forms | 28560 | 2400 | 26160 |
| Eisenstein series | 480 | 0 | 480 |
Decomposition of \(S_{2}^{\mathrm{new}}(8004, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8004, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8004, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(667, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1334, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2001, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2668, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4002, [\chi])\)\(^{\oplus 2}\)