Base field \(\Q(\sqrt{5}, \sqrt{17})\)
Generator \(w\), with minimal polynomial \(x^{4} - 11x^{2} + 9\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 3x - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{3}{2}]$ | $-1$ |
4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{3}{2}]$ | $-1$ |
9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{11}{3}w]$ | $\phantom{-}e$ |
9 | $[9, 3, w]$ | $\phantom{-}e$ |
19 | $[19, 19, w + 2]$ | $-e + 4$ |
19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w - 2]$ | $-e + 4$ |
19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w + 2]$ | $-e + 4$ |
19 | $[19, 19, -w + 2]$ | $-e + 4$ |
25 | $[25, 5, \frac{1}{3}w^{3} - \frac{8}{3}w]$ | $\phantom{-}10$ |
49 | $[49, 7, \frac{2}{3}w^{3} - \frac{19}{3}w]$ | $-2e + 8$ |
49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{5}{3}w]$ | $-2e + 8$ |
59 | $[59, 59, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{11}{6}w]$ | $\phantom{-}e + 4$ |
59 | $[59, 59, \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{11}{2}]$ | $\phantom{-}e + 4$ |
59 | $[59, 59, \frac{1}{2}w^{2} - \frac{1}{2}w - \frac{11}{2}]$ | $\phantom{-}e + 4$ |
59 | $[59, 59, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} - \frac{11}{6}w]$ | $\phantom{-}e + 4$ |
89 | $[89, 89, \frac{2}{3}w^{3} + \frac{1}{2}w^{2} - \frac{35}{6}w - \frac{7}{2}]$ | $\phantom{-}e - 8$ |
89 | $[89, 89, -\frac{5}{6}w^{3} + \frac{26}{3}w - \frac{3}{2}]$ | $\phantom{-}e - 8$ |
89 | $[89, 89, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} + \frac{1}{6}w - 2]$ | $\phantom{-}e - 8$ |
89 | $[89, 89, -\frac{1}{6}w^{3} - w^{2} + \frac{7}{3}w + \frac{5}{2}]$ | $\phantom{-}e - 8$ |
101 | $[101, 101, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{17}{6}w + 1]$ | $-12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,\frac{1}{6}w^{3}-\frac{7}{3}w-\frac{3}{2}]$ | $1$ |
$4$ | $[4,2,\frac{1}{6}w^{3}-\frac{7}{3}w+\frac{3}{2}]$ | $1$ |