Properties

Label 4.4.12544.1-7.1-b
Base field \(\Q(\sqrt{2}, \sqrt{7})\)
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, \frac{1}{3}w^{3} - \frac{8}{3}w + 2]$
Dimension $2$
CM no
Base change no

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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: $[7, 7, \frac{1}{3}w^{3} - \frac{8}{3}w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 8\)

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

Atkin-Lehner eigenvalues

The Atkin-Lehner eigenvalues for this form are not in the database.