Defining parameters
Level: | \( N \) | \(=\) | \( 992 = 2^{5} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 992.y (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 992 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(992, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 8 | 8 | 0 |
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 \(S_{1}^{\mathrm{new}}(992, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
992.1.y.a | $4$ | $0.495$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-31}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q-\zeta_{8}^{2}q^{2}-q^{4}+(1-\zeta_{8})q^{5}+\zeta_{8}^{2}q^{8}+\cdots\) |
992.1.y.b | $8$ | $0.495$ | \(\Q(\zeta_{24})\) | $D_{24}$ | \(\Q(\sqrt{-31}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+(-\zeta_{24}+\zeta_{24}^{8}+\cdots)q^{5}+\cdots\) |