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: | $[89,89,2w^{4} - w^{3} - 6w^{2} + 2w + 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 16x - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $\phantom{-}e$ |
23 | $[23, 23, -w^{4} + 3w^{2} + 1]$ | $-\frac{1}{4}e^{2} + \frac{1}{2}e + 4$ |
23 | $[23, 23, -w^{4} + 3w^{2} + w - 2]$ | $-e^{2} + 3e + 12$ |
23 | $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 8$ |
23 | $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-\frac{1}{4}e^{2}$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{4}e^{2} - \frac{5}{2}e - 2$ |
32 | $[32, 2, 2]$ | $\phantom{-}\frac{5}{4}e^{2} - 2e - 13$ |
43 | $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ | $-\frac{1}{2}e^{2} - e + 8$ |
43 | $[43, 43, -w^{4} + 2w^{2} + w + 1]$ | $\phantom{-}\frac{3}{4}e^{2} - 4$ |
43 | $[43, 43, w^{3} + w^{2} - 4w - 2]$ | $-e^{2} + 8$ |
43 | $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ | $-\frac{1}{2}e^{2} + e + 4$ |
43 | $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ | $\phantom{-}\frac{1}{4}e^{2} - \frac{1}{2}e + 4$ |
67 | $[67, 67, 2w^{4} - 7w^{2} + 2]$ | $\phantom{-}\frac{3}{4}e^{2} + \frac{1}{2}e - 6$ |
67 | $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 2e$ |
67 | $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ | $\phantom{-}\frac{3}{4}e^{2} - \frac{7}{2}e - 8$ |
67 | $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ | $-\frac{1}{2}e^{2} + e + 8$ |
67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{7}{4}e^{2} - \frac{1}{2}e - 18$ |
89 | $[89, 89, w^{3} + w^{2} - 4w - 1]$ | $-\frac{1}{4}e^{2} + \frac{1}{2}e$ |
89 | $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ | $-\frac{5}{4}e^{2} + \frac{1}{2}e + 14$ |
89 | $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ | $-e^{2} + 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$89$ | $[89,89,2w^{4} - w^{3} - 6w^{2} + 2w + 2]$ | $-1$ |