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: | $[36,6,\frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{11}{6}w - 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 16x^{4} + 8x^{3} + 51x^{2} - 24x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{3}{2}]$ | $\phantom{-}e$ |
4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{3}{2}]$ | $\phantom{-}1$ |
9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{11}{3}w]$ | $\phantom{-}1$ |
9 | $[9, 3, w]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{9}{2}e + 3$ |
19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{1}{2}e^{4} + e^{3} - \frac{9}{2}e^{2} - 4e + 3$ |
19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w - 2]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 7e^{3} + \frac{3}{2}e^{2} - \frac{41}{2}e + 5$ |
19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w + 2]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{11}{2}e^{2} - \frac{3}{2}e + 6$ |
19 | $[19, 19, -w + 2]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{9}{2}e^{2} + \frac{21}{2}e - 5$ |
25 | $[25, 5, \frac{1}{3}w^{3} - \frac{8}{3}w]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 7e^{3} + \frac{3}{2}e^{2} - \frac{37}{2}e + 1$ |
49 | $[49, 7, \frac{2}{3}w^{3} - \frac{19}{3}w]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - \frac{13}{2}e^{3} - \frac{1}{2}e^{2} + 17e - 5$ |
49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{5}{3}w]$ | $\phantom{-}\frac{1}{2}e^{5} - 8e^{3} + 4e^{2} + \frac{47}{2}e - 10$ |
59 | $[59, 59, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{11}{6}w]$ | $-\frac{1}{2}e^{5} - e^{4} + 6e^{3} + 5e^{2} - \frac{31}{2}e + 10$ |
59 | $[59, 59, \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{11}{2}]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{17}{2}e^{3} + 3e^{2} + 28e - 7$ |
59 | $[59, 59, \frac{1}{2}w^{2} - \frac{1}{2}w - \frac{11}{2}]$ | $\phantom{-}\frac{1}{2}e^{5} + e^{4} - 6e^{3} - 6e^{2} + \frac{27}{2}e + 1$ |
59 | $[59, 59, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} - \frac{11}{6}w]$ | $-e^{3} + 9e - 4$ |
89 | $[89, 89, \frac{2}{3}w^{3} + \frac{1}{2}w^{2} - \frac{35}{6}w - \frac{7}{2}]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - \frac{15}{2}e^{3} - \frac{3}{2}e^{2} + 26e - 4$ |
89 | $[89, 89, -\frac{5}{6}w^{3} + \frac{26}{3}w - \frac{3}{2}]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{19}{2}e^{3} - \frac{15}{2}e^{2} - 34e + 6$ |
89 | $[89, 89, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} + \frac{1}{6}w - 2]$ | $\phantom{-}e^{5} + 2e^{4} - 11e^{3} - 11e^{2} + 20e + 1$ |
89 | $[89, 89, -\frac{1}{6}w^{3} - w^{2} + \frac{7}{3}w + \frac{5}{2}]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{11}{2}e^{2} + 7e - 5$ |
101 | $[101, 101, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{17}{6}w + 1]$ | $-\frac{1}{2}e^{5} - e^{4} + 5e^{3} + 4e^{2} - \frac{9}{2}e + 3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,\frac{1}{6}w^{3} - \frac{7}{3}w + \frac{3}{2}]$ | $-1$ |
$9$ | $[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w]$ | $-1$ |