Properties

Label 4.4.4525.1-16.1-a
Base field 4.4.4525.1
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 4.4.4525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 3x + 9\); narrow class number \(1\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 3x^{3} - 7x^{2} + 14x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $\phantom{-}e$
9 $[9, 3, -w]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e - 1$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e - 1$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{7}{2}e^{2} - \frac{23}{2}e + 10$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{7}{2}e^{2} - \frac{23}{2}e + 10$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $\phantom{-}e^{3} - 3e^{2} - 9e + 12$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $\phantom{-}e^{3} - 3e^{2} - 9e + 12$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{5}{2}e - 4$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{5}{2}e - 4$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $\phantom{-}e^{3} - 3e^{2} - 8e + 2$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $\phantom{-}e^{3} - 3e^{2} - 8e + 2$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $-3e^{3} + 7e^{2} + 25e - 22$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-3e^{3} + 7e^{2} + 25e - 22$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{11}{2}e^{2} - \frac{45}{2}e + 19$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{11}{2}e^{2} - \frac{45}{2}e + 19$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $\phantom{-}e^{3} - e^{2} - 14e + 6$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $-e^{3} + 2e^{2} + 9e - 12$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $-e^{3} + 2e^{2} + 9e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$