Properties

Label 4.4.7225.1-16.1-d
Base field \(\Q(\sqrt{5}, \sqrt{17})\)
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $2$
CM no
Base change yes

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Base field \(\Q(\sqrt{5}, \sqrt{17})\)

Generator \(w\), with minimal polynomial \(x^{4} - 11x^{2} + 9\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $2$
CM: no
Base change: yes
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 3x - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{3}{2}]$ $-1$
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{3}{2}]$ $-1$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{11}{3}w]$ $\phantom{-}e$
9 $[9, 3, w]$ $\phantom{-}e$
19 $[19, 19, w + 2]$ $-e + 4$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w - 2]$ $-e + 4$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w + 2]$ $-e + 4$
19 $[19, 19, -w + 2]$ $-e + 4$
25 $[25, 5, \frac{1}{3}w^{3} - \frac{8}{3}w]$ $\phantom{-}10$
49 $[49, 7, \frac{2}{3}w^{3} - \frac{19}{3}w]$ $-2e + 8$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{5}{3}w]$ $-2e + 8$
59 $[59, 59, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{11}{6}w]$ $\phantom{-}e + 4$
59 $[59, 59, \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{11}{2}]$ $\phantom{-}e + 4$
59 $[59, 59, \frac{1}{2}w^{2} - \frac{1}{2}w - \frac{11}{2}]$ $\phantom{-}e + 4$
59 $[59, 59, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} - \frac{11}{6}w]$ $\phantom{-}e + 4$
89 $[89, 89, \frac{2}{3}w^{3} + \frac{1}{2}w^{2} - \frac{35}{6}w - \frac{7}{2}]$ $\phantom{-}e - 8$
89 $[89, 89, -\frac{5}{6}w^{3} + \frac{26}{3}w - \frac{3}{2}]$ $\phantom{-}e - 8$
89 $[89, 89, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} + \frac{1}{6}w - 2]$ $\phantom{-}e - 8$
89 $[89, 89, -\frac{1}{6}w^{3} - w^{2} + \frac{7}{3}w + \frac{5}{2}]$ $\phantom{-}e - 8$
101 $[101, 101, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{17}{6}w + 1]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{6}w^{3}-\frac{7}{3}w-\frac{3}{2}]$ $1$
$4$ $[4,2,\frac{1}{6}w^{3}-\frac{7}{3}w+\frac{3}{2}]$ $1$