Defining parameters
| Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3969.f (of order \(3\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
| Character field: | \(\Q(\zeta_{3})\) | ||
| Sturm bound: | \(1008\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3969, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1104 | 338 | 766 |
| Cusp forms | 912 | 318 | 594 |
| Eisenstein series | 192 | 20 | 172 |
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
\( S_{2}^{\mathrm{old}}(3969, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)