Properties

Label 4.4.9225.1-16.1-a
Base field 4.4.9225.1
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 4.4.9225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 10x^{2} + 7x + 19\); 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: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 13x^{2} + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ $-1$
4 $[4, 2, \frac{1}{2}w^{3} - 4w - \frac{1}{2}]$ $-1$
9 $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$
11 $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{7}{4}]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{3}{2}]$ $\phantom{-}e$
19 $[19, 19, w]$ $-e^{2} + 4$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{5}{2}w + \frac{1}{4}]$ $-e^{2} + 4$
25 $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ $-e^{2} + 10$
29 $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$
29 $[29, 29, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{9}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$
41 $[41, 41, -w^{3} + 7w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e$
41 $[41, 41, -\frac{3}{4}w^{3} + \frac{11}{2}w - \frac{3}{4}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e$
41 $[41, 41, \frac{1}{4}w^{3} + w^{2} - \frac{5}{2}w - \frac{11}{4}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e$
71 $[71, 71, \frac{1}{2}w^{3} - 4w + \frac{5}{2}]$ $-4e$
71 $[71, 71, \frac{3}{4}w^{3} + w^{2} - \frac{11}{2}w - \frac{21}{4}]$ $-4e$
79 $[79, 79, \frac{1}{4}w^{3} - 2w^{2} + \frac{1}{2}w + \frac{25}{4}]$ $-2e^{2} + 8$
79 $[79, 79, -\frac{3}{4}w^{3} + \frac{13}{2}w + \frac{9}{4}]$ $-2e^{2} + 8$
89 $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{41}{4}]$ $-\frac{1}{2}e^{3} + \frac{19}{2}e$
89 $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{33}{4}]$ $-\frac{1}{2}e^{3} + \frac{19}{2}e$
101 $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{1}{2}w - \frac{27}{4}]$ $-\frac{1}{2}e^{3} + \frac{21}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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