Properties

Label 4.4.19025.1-16.1-c
Base field 4.4.19025.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $5$
CM no
Base change yes

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Base field 4.4.19025.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $5$
CM: no
Base change: yes
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} + 3x^{4} - 11x^{3} - 21x^{2} + 34x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}1$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $-\frac{1}{3}e^{4} - \frac{2}{3}e^{3} + \frac{10}{3}e^{2} + \frac{11}{3}e - 5$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $-\frac{1}{3}e^{4} - \frac{2}{3}e^{3} + \frac{10}{3}e^{2} + \frac{11}{3}e - 5$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{2}{3}e^{3} - \frac{7}{3}e^{2} - \frac{5}{3}e + 1$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{2}{3}e^{3} - \frac{7}{3}e^{2} - \frac{5}{3}e + 1$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $\phantom{-}e^{2} + e$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $-2e^{2} - 3e + 9$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $-2e^{2} - 3e + 9$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $\phantom{-}e^{2} + e$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $\phantom{-}\frac{2}{3}e^{4} + \frac{7}{3}e^{3} - \frac{17}{3}e^{2} - \frac{46}{3}e + 15$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $\phantom{-}\frac{2}{3}e^{4} + \frac{7}{3}e^{3} - \frac{17}{3}e^{2} - \frac{46}{3}e + 15$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $-e^{4} - 3e^{3} + 9e^{2} + 18e - 15$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $-e^{4} - 3e^{3} + 9e^{2} + 18e - 15$
81 $[81, 3, -3]$ $\phantom{-}\frac{2}{3}e^{4} + \frac{7}{3}e^{3} - \frac{14}{3}e^{2} - \frac{49}{3}e + 5$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $-\frac{2}{3}e^{4} - \frac{10}{3}e^{3} + \frac{14}{3}e^{2} + \frac{64}{3}e - 16$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $\phantom{-}2e^{2} + 5e - 12$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $\phantom{-}2e^{2} + 5e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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