Properties

Label 4.4.7225.1-36.3-f
Base field \(\Q(\sqrt{5}, \sqrt{17})\)
Weight $[2, 2, 2, 2]$
Level norm $36$
Level $[36,6,\frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{11}{6}w - 1]$
Dimension $2$
CM no
Base change no

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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: $[36,6,\frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{11}{6}w - 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $15$

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{6}w^{3} - \frac{7}{3}w + \frac{3}{2}]$ $1$
$9$ $[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w]$ $-1$