Base field \(\Q(\sqrt{2}, \sqrt{17})\)
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8,4,\frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{5}{9}w + \frac{5}{9}]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 20x^{2} + 32\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{47}{9}w + \frac{20}{9}]$ | $\phantom{-}\frac{1}{4}e^{2} - 2$ |
2 | $[2, 2, \frac{5}{9}w^{3} - \frac{4}{3}w^{2} - \frac{52}{9}w + \frac{79}{9}]$ | $\phantom{-}0$ |
9 | $[9, 3, \frac{1}{3}w^{3} - \frac{11}{3}w - \frac{1}{3}]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - w^{2} - 12w - 1]$ | $-e$ |
17 | $[17, 17, -\frac{1}{9}w^{3} - \frac{1}{3}w^{2} + \frac{14}{9}w + \frac{49}{9}]$ | $-\frac{1}{4}e^{3} + 4e$ |
17 | $[17, 17, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{59}{9}]$ | $\phantom{-}\frac{1}{4}e^{3} - 4e$ |
25 | $[25, 5, -\frac{7}{9}w^{3} + \frac{2}{3}w^{2} + \frac{89}{9}w + \frac{19}{9}]$ | $\phantom{-}\frac{1}{4}e^{3} - 4e$ |
25 | $[25, 5, -\frac{5}{9}w^{3} + \frac{1}{3}w^{2} + \frac{52}{9}w + \frac{11}{9}]$ | $-\frac{1}{4}e^{3} + 4e$ |
47 | $[47, 47, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{41}{9}]$ | $\phantom{-}0$ |
47 | $[47, 47, \frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{14}{9}w - \frac{13}{9}]$ | $\phantom{-}\frac{1}{2}e^{2} - 6$ |
47 | $[47, 47, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{23}{9}]$ | $\phantom{-}0$ |
47 | $[47, 47, \frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{14}{9}w - \frac{31}{9}]$ | $\phantom{-}\frac{1}{2}e^{2} - 6$ |
49 | $[49, 7, -\frac{4}{9}w^{3} + \frac{2}{3}w^{2} + \frac{38}{9}w - \frac{29}{9}]$ | $\phantom{-}\frac{1}{2}e^{2}$ |
49 | $[49, 7, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{38}{9}w + \frac{11}{9}]$ | $\phantom{-}\frac{1}{2}e^{2}$ |
89 | $[89, 89, \frac{20}{9}w^{3} - \frac{16}{3}w^{2} - \frac{208}{9}w + \frac{325}{9}]$ | $\phantom{-}\frac{1}{2}e^{2}$ |
89 | $[89, 89, \frac{2}{3}w^{3} - w^{2} - \frac{25}{3}w + \frac{7}{3}]$ | $-\frac{3}{2}e^{2} + 16$ |
89 | $[89, 89, -\frac{2}{3}w^{3} + w^{2} + \frac{25}{3}w - \frac{19}{3}]$ | $\phantom{-}\frac{1}{2}e^{2}$ |
89 | $[89, 89, -2w^{3} + 3w^{2} + 23w - 11]$ | $-\frac{3}{2}e^{2} + 16$ |
103 | $[103, 103, \frac{8}{9}w^{3} - \frac{4}{3}w^{2} - \frac{94}{9}w + \frac{67}{9}]$ | $\phantom{-}\frac{1}{2}e^{3} - 6e$ |
103 | $[103, 103, -\frac{38}{9}w^{3} + \frac{28}{3}w^{2} + \frac{406}{9}w - \frac{541}{9}]$ | $-\frac{1}{2}e^{3} + 6e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-\frac{4}{9}w^{3} + \frac{2}{3}w^{2} + \frac{47}{9}w - \frac{29}{9}]$ | $1$ |