Defining parameters
| Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8048.m (of order \(251\) and degree \(250\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 503 \) |
| Character field: | \(\Q(\zeta_{251})\) | ||
| Sturm bound: | \(2016\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8048, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 253500 | 63250 | 190250 |
| Cusp forms | 250500 | 62750 | 187750 |
| Eisenstein series | 3000 | 500 | 2500 |
Decomposition of \(S_{2}^{\mathrm{new}}(8048, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8048, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8048, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(503, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1006, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2012, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4024, [\chi])\)\(^{\oplus 2}\)