Base field \(\Q(\zeta_{11})^+\)
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $-3$ |
23 | $[23, 23, -w^{4} + 3w^{2} + 1]$ | $\phantom{-}4$ |
23 | $[23, 23, -w^{4} + 3w^{2} + w - 2]$ | $\phantom{-}4$ |
23 | $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}4$ |
23 | $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-1$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $-1$ |
32 | $[32, 2, 2]$ | $\phantom{-}3$ |
43 | $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ | $\phantom{-}1$ |
43 | $[43, 43, -w^{4} + 2w^{2} + w + 1]$ | $-1$ |
43 | $[43, 43, w^{3} + w^{2} - 4w - 2]$ | $\phantom{-}4$ |
43 | $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ | $-11$ |
43 | $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ | $\phantom{-}9$ |
67 | $[67, 67, 2w^{4} - 7w^{2} + 2]$ | $-2$ |
67 | $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ | $-12$ |
67 | $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ | $\phantom{-}13$ |
67 | $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ | $-2$ |
67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-2$ |
89 | $[89, 89, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}0$ |
89 | $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ | $-10$ |
89 | $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ | $\phantom{-}15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$43$ | $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ | $-1$ |