Defining parameters
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 983 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(82\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(983, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 14 | 0 |
Cusp forms | 13 | 13 | 0 |
Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 13 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(983, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
983.1.b.a | $1$ | $0.491$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-983}) \) | None | \(-1\) | \(-1\) | \(0\) | \(-1\) | \(q-q^{2}-q^{3}+q^{6}-q^{7}+q^{8}+q^{14}+\cdots\) |
983.1.b.b | $3$ | $0.491$ | \(\Q(\zeta_{18})^+\) | $D_{9}$ | \(\Q(\sqrt{-983}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\) |
983.1.b.c | $9$ | $0.491$ | \(\Q(\zeta_{54})^+\) | $D_{27}$ | \(\Q(\sqrt{-983}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\) |