Defining parameters
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.bz (of order \(42\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 441 \) |
Character field: | \(\Q(\zeta_{42})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(504\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3969, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 36 | 120 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 144 | 24 | 120 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3969.1.bz.a | $12$ | $1.981$ | \(\Q(\zeta_{21})\) | $D_{14}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(-1\) | \(q-\zeta_{42}^{16}q^{4}-\zeta_{42}^{8}q^{7}+(-\zeta_{42}^{4}+\cdots)q^{13}+\cdots\) |