Base field \(\Q(\sqrt{5}, \sqrt{13})\)
Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[36,6,-\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{9}{4}w + \frac{1}{2}]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - x^{2} - 7x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w]$ | $\phantom{-}e$ |
4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{9}{2}w]$ | $\phantom{-}1$ |
9 | $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w - \frac{1}{2}]$ | $\phantom{-}e^{2} - 2e - 5$ |
9 | $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w + \frac{1}{2}]$ | $\phantom{-}1$ |
25 | $[25, 5, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $-e - 1$ |
29 | $[29, 29, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{9}{4}w - \frac{1}{2}]$ | $-e^{2} + 3e + 8$ |
29 | $[29, 29, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ | $-e + 3$ |
29 | $[29, 29, -\frac{1}{2}w^{2} + \frac{1}{2}w + 4]$ | $-2e^{2} + 2e + 6$ |
29 | $[29, 29, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{9}{4}w + \frac{1}{2}]$ | $\phantom{-}2e^{2} - 2e - 10$ |
49 | $[49, 7, \frac{3}{4}w^{3} + \frac{1}{2}w^{2} - \frac{23}{4}w - \frac{3}{2}]$ | $\phantom{-}3e + 3$ |
49 | $[49, 7, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ | $-e^{2} + 11$ |
61 | $[61, 61, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 1]$ | $-2$ |
61 | $[61, 61, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{13}{4}w + \frac{7}{2}]$ | $-e^{2} + 4e + 3$ |
61 | $[61, 61, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{13}{4}w - \frac{7}{2}]$ | $-2e^{2} + e + 11$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 1]$ | $-2$ |
79 | $[79, 79, \frac{3}{4}w^{3} - \frac{25}{4}w - \frac{9}{2}]$ | $\phantom{-}2e^{2} + e - 7$ |
79 | $[79, 79, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{3}{4}w - \frac{3}{2}]$ | $-3e - 1$ |
79 | $[79, 79, \frac{1}{4}w^{3} - \frac{3}{4}w - \frac{9}{2}]$ | $-3e^{2} + 2e + 17$ |
79 | $[79, 79, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 13w - 3]$ | $-2e^{2} - 2e + 12$ |
101 | $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{7}{4}w - \frac{5}{2}]$ | $\phantom{-}3e^{2} - 4e - 17$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,\frac{1}{2}w^{3} - \frac{9}{2}w]$ | $-1$ |
$9$ | $[9,3,-\frac{1}{4}w^{3} + \frac{11}{4}w - \frac{1}{2}]$ | $-1$ |