Defining parameters
| Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3969.u (of order \(7\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
| Character field: | \(\Q(\zeta_{7})\) | ||
| Sturm bound: | \(1008\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3969, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3096 | 1368 | 1728 |
| Cusp forms | 2952 | 1320 | 1632 |
| Eisenstein series | 144 | 48 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3969, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)