Defining parameters
| Level: | \( N \) | \(=\) | \( 4160 = 2^{6} \cdot 5 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4160.bj (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(1344\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4160, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1376 | 192 | 1184 |
| Cusp forms | 1312 | 192 | 1120 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{2}^{\mathrm{new}}(4160, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4160, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 3}\)