Base field 4.4.18432.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 2]$ |
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:
\(x^{4} - 12x^{2} - 16x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $\phantom{-}0$ |
7 | $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $\phantom{-}e$ |
7 | $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ | $-\frac{1}{2}e^{3} + 6e + 6$ |
7 | $[7, 7, \frac{1}{3}w^{2} + w - 1]$ | $-\frac{1}{2}e^{3} + e^{2} + 4e$ |
7 | $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ | $\phantom{-}e^{3} - e^{2} - 11e - 6$ |
9 | $[9, 3, w - 3]$ | $\phantom{-}0$ |
41 | $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $\phantom{-}e^{3} + e^{2} - 14e - 14$ |
41 | $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ | $\phantom{-}e^{3} - e^{2} - 14e - 2$ |
41 | $[41, 41, \frac{1}{3}w^{2} + w - 3]$ | $-3e^{3} + 3e^{2} + 34e + 22$ |
41 | $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ | $\phantom{-}e^{3} - 3e^{2} - 6e + 10$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ | $\phantom{-}e^{3} - 2e^{2} - 6e + 4$ |
47 | $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ | $-e^{3} + 10e + 16$ |
47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $-3e^{3} + 4e^{2} + 30e + 16$ |
47 | $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $\phantom{-}3e^{3} - 2e^{2} - 34e - 20$ |
89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ | $-2e^{3} + 4e^{2} + 16e$ |
89 | $[89, 89, \frac{2}{3}w^{2} + w - 5]$ | $\phantom{-}4e$ |
89 | $[89, 89, \frac{2}{3}w^{2} - w - 5]$ | $\phantom{-}4e^{3} - 4e^{2} - 44e - 24$ |
89 | $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ | $-2e^{3} + 24e + 24$ |
97 | $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ | $-2e^{3} + 3e^{2} + 22e + 2$ |
97 | $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ | $\phantom{-}e^{3} + e^{2} - 16e - 22$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $1$ |