Defining parameters
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.w (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 68 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(504\) | ||
Trace bound: | \(20\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 56 | 24 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 64 | 40 | 24 |
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 \(S_{1}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3332.1.w.a | $4$ | $1.663$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{5}+\cdots\) |
3332.1.w.b | $4$ | $1.663$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\) |
3332.1.w.c | $4$ | $1.663$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\) |
3332.1.w.d | $4$ | $1.663$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{3})q^{5}-\zeta_{8}^{3}q^{8}+\cdots\) |