Properties

Label 4.4.12544.1-8.1-a
Base field \(\Q(\sqrt{2}, \sqrt{7})\)
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 2, -\frac{1}{3}w^{3} - w^{2} - \frac{1}{3}w + 1]$
Dimension $2$
CM no
Base change yes

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Base field \(\Q(\sqrt{2}, \sqrt{7})\)

Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 9\); narrow class number \(4\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 2, -\frac{1}{3}w^{3} - w^{2} - \frac{1}{3}w + 1]$
Dimension: $2$
CM: no
Base change: yes
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} - 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - 2]$ $\phantom{-}0$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{8}{3}w + 2]$ $\phantom{-}0$
7 $[7, 7, -w + 2]$ $\phantom{-}0$
9 $[9, 3, w]$ $-2$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{8}{3}w]$ $-2$
25 $[25, 5, \frac{1}{3}w^{3} - w^{2} - \frac{5}{3}w + 4]$ $-2$
25 $[25, 5, -\frac{1}{3}w^{3} - w^{2} + \frac{5}{3}w + 4]$ $-2$
31 $[31, 31, \frac{1}{3}w^{3} + w^{2} - \frac{5}{3}w - 2]$ $-e$
31 $[31, 31, \frac{1}{3}w^{3} + w^{2} - \frac{5}{3}w - 6]$ $-e$
31 $[31, 31, \frac{1}{3}w^{3} - w^{2} - \frac{5}{3}w + 6]$ $\phantom{-}e$
31 $[31, 31, \frac{1}{3}w^{3} - w^{2} - \frac{5}{3}w + 2]$ $\phantom{-}e$
47 $[47, 47, \frac{1}{3}w^{3} + w^{2} - \frac{8}{3}w - 3]$ $\phantom{-}e$
47 $[47, 47, -w^{2} - w + 5]$ $\phantom{-}e$
47 $[47, 47, w^{2} - w - 5]$ $-e$
47 $[47, 47, -\frac{1}{3}w^{3} + w^{2} + \frac{8}{3}w - 3]$ $-e$
103 $[103, 103, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - 2]$ $\phantom{-}3e$
103 $[103, 103, -\frac{2}{3}w^{3} + w^{2} + \frac{10}{3}w - 6]$ $-3e$
103 $[103, 103, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - 6]$ $\phantom{-}3e$
103 $[103, 103, \frac{1}{3}w^{3} + 2w^{2} + \frac{7}{3}w - 1]$ $-3e$
113 $[113, 113, -\frac{2}{3}w^{3} + \frac{16}{3}w + 1]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,\frac{1}{3}w^{3}+w^{2}-\frac{2}{3}w-2]$ $-1$