Properties

Label 4.4.17424.1-8.3-a
Base field \(\Q(\sqrt{3}, \sqrt{11})\)
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 4, w + 2]$
Dimension $2$
CM no
Base change yes

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Base field \(\Q(\sqrt{3}, \sqrt{11})\)

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 4, w + 2]$
Dimension: $2$
CM: no
Base change: yes
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{3} + \frac{7}{2}w - 1]$ $\phantom{-}0$
2 $[2, 2, -w + 1]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w]$ $\phantom{-}e - 1$
11 $[11, 11, -w^{2} + w + 1]$ $-4$
11 $[11, 11, w^{2} + w - 1]$ $-4$
25 $[25, 5, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ $\phantom{-}e - 1$
25 $[25, 5, -\frac{1}{2}w^{3} - w^{2} + \frac{7}{2}w + 4]$ $\phantom{-}e - 1$
37 $[37, 37, -w^{3} + 7w + 1]$ $\phantom{-}3e + 5$
37 $[37, 37, -2w + 1]$ $-e + 1$
37 $[37, 37, 2w + 1]$ $-e + 1$
37 $[37, 37, -w^{3} + 7w - 1]$ $\phantom{-}3e + 5$
49 $[49, 7, \frac{1}{2}w^{3} - \frac{9}{2}w + 2]$ $-4e - 2$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{9}{2}w + 2]$ $-4e - 2$
83 $[83, 83, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 2]$ $\phantom{-}4$
83 $[83, 83, w^{2} + w - 5]$ $\phantom{-}4$
83 $[83, 83, w^{2} - w - 5]$ $\phantom{-}4$
83 $[83, 83, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 2]$ $\phantom{-}4$
97 $[97, 97, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 8]$ $-5e - 7$
97 $[97, 97, \frac{5}{2}w^{3} - w^{2} - \frac{31}{2}w + 6]$ $\phantom{-}3e + 1$
97 $[97, 97, -\frac{11}{2}w^{3} + 4w^{2} + \frac{71}{2}w - 26]$ $\phantom{-}3e + 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-\frac{1}{2}w^{3}+\frac{7}{2}w-1]$ $-1$