Defining parameters
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.q (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
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 | 128 | 24 | 104 |
Cusp forms | 32 | 8 | 24 |
Eisenstein series | 96 | 16 | 80 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 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.q.a | $8$ | $1.981$ | \(\Q(\zeta_{24})\) | $D_{12}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)