Properties

Label 4.4.19025.1-5.2-c
Base field 4.4.19025.1
Weight $[2, 2, 2, 2]$
Level norm $5$
Level $[5,5,\frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$
Dimension $2$
CM no
Base change no

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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: $[5,5,\frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 3x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $-2$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $\phantom{-}e - 3$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $\phantom{-}1$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $\phantom{-}2e - 7$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $-3e + 5$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $-6e + 9$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $\phantom{-}5e - 13$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $-9e + 14$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $\phantom{-}2e + 1$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $-2e + 4$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $\phantom{-}e + 1$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $-e + 6$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $-8e + 14$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $-2e + 8$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $\phantom{-}6e - 9$
81 $[81, 3, -3]$ $-1$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $\phantom{-}5e - 8$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $-4e$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $\phantom{-}6e - 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,\frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $-1$