Defining parameters
| Level: | \( N \) | \(=\) | \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4680.db (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(2016\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4680, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2080 | 210 | 1870 |
| Cusp forms | 1952 | 210 | 1742 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{2}^{\mathrm{new}}(4680, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4680, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4680, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2340, [\chi])\)\(^{\oplus 2}\)