Defining parameters
| Level: | \( N \) | \(=\) | \( 5312 = 2^{6} \cdot 83 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5312.u (of order \(41\) and degree \(40\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 83 \) |
| Character field: | \(\Q(\zeta_{41})\) | ||
| Sturm bound: | \(1344\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5312, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 27360 | 6800 | 20560 |
| Cusp forms | 26400 | 6640 | 19760 |
| Eisenstein series | 960 | 160 | 800 |
Decomposition of \(S_{2}^{\mathrm{new}}(5312, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(5312, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5312, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(83, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(166, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(332, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(664, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1328, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2656, [\chi])\)\(^{\oplus 2}\)