Properties

Label 4.4.18496.1-16.1-c
Base field \(\Q(\sqrt{2}, \sqrt{17})\)
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $4$
CM no
Base change yes

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Base field \(\Q(\sqrt{2}, \sqrt{17})\)

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $4$
CM: no
Base change: yes
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 72x^{2} + 400\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{47}{9}w + \frac{20}{9}]$ $\phantom{-}0$
2 $[2, 2, \frac{5}{9}w^{3} - \frac{4}{3}w^{2} - \frac{52}{9}w + \frac{79}{9}]$ $\phantom{-}0$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{11}{3}w - \frac{1}{3}]$ $-\frac{1}{80}e^{3} + \frac{13}{20}e$
9 $[9, 3, w^{3} - w^{2} - 12w - 1]$ $-\frac{1}{80}e^{3} + \frac{13}{20}e$
17 $[17, 17, -\frac{1}{9}w^{3} - \frac{1}{3}w^{2} + \frac{14}{9}w + \frac{49}{9}]$ $\phantom{-}e$
17 $[17, 17, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{59}{9}]$ $\phantom{-}\frac{1}{20}e^{3} - \frac{18}{5}e$
25 $[25, 5, -\frac{7}{9}w^{3} + \frac{2}{3}w^{2} + \frac{89}{9}w + \frac{19}{9}]$ $-\frac{1}{20}e^{3} + \frac{13}{5}e$
25 $[25, 5, -\frac{5}{9}w^{3} + \frac{1}{3}w^{2} + \frac{52}{9}w + \frac{11}{9}]$ $-\frac{1}{20}e^{3} + \frac{13}{5}e$
47 $[47, 47, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{41}{9}]$ $\phantom{-}\frac{1}{4}e^{2} - 7$
47 $[47, 47, \frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{14}{9}w - \frac{13}{9}]$ $\phantom{-}\frac{1}{4}e^{2} - 7$
47 $[47, 47, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} + \frac{5}{9}w - \frac{23}{9}]$ $-\frac{1}{4}e^{2} + 11$
47 $[47, 47, \frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{14}{9}w - \frac{31}{9}]$ $-\frac{1}{4}e^{2} + 11$
49 $[49, 7, -\frac{4}{9}w^{3} + \frac{2}{3}w^{2} + \frac{38}{9}w - \frac{29}{9}]$ $\phantom{-}\frac{1}{8}e^{2} + \frac{11}{2}$
49 $[49, 7, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{38}{9}w + \frac{11}{9}]$ $-\frac{1}{8}e^{2} + \frac{29}{2}$
89 $[89, 89, \frac{20}{9}w^{3} - \frac{16}{3}w^{2} - \frac{208}{9}w + \frac{325}{9}]$ $-\frac{3}{8}e^{2} + \frac{23}{2}$
89 $[89, 89, \frac{2}{3}w^{3} - w^{2} - \frac{25}{3}w + \frac{7}{3}]$ $-\frac{3}{8}e^{2} + \frac{23}{2}$
89 $[89, 89, -\frac{2}{3}w^{3} + w^{2} + \frac{25}{3}w - \frac{19}{3}]$ $\phantom{-}\frac{3}{8}e^{2} - \frac{31}{2}$
89 $[89, 89, -2w^{3} + 3w^{2} + 23w - 11]$ $\phantom{-}\frac{3}{8}e^{2} - \frac{31}{2}$
103 $[103, 103, \frac{8}{9}w^{3} - \frac{4}{3}w^{2} - \frac{94}{9}w + \frac{67}{9}]$ $\phantom{-}\frac{1}{40}e^{3} - \frac{33}{10}e$
103 $[103, 103, -\frac{38}{9}w^{3} + \frac{28}{3}w^{2} + \frac{406}{9}w - \frac{541}{9}]$ $-\frac{3}{40}e^{3} + \frac{59}{10}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{47}{9}w + \frac{20}{9}]$ $-1$
$2$ $[2, 2, \frac{5}{9}w^{3} - \frac{4}{3}w^{2} - \frac{52}{9}w + \frac{79}{9}]$ $-1$