Defining parameters
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.r (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(504\) | ||
Trace bound: | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3969, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 26 | 86 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 96 | 10 | 86 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 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.r.a | $2$ | $1.981$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}-q^{19}+\cdots\) |
3969.1.r.b | $2$ | $1.981$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+q^{19}+\cdots\) |
3969.1.r.c | $4$ | $1.981$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | $D_{4}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{11}+\cdots\) |
3969.1.r.d | $8$ | $1.981$ | \(\Q(\zeta_{24})\) | $D_{12}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\) |