Properties

Label 4.4.8000.1-44.1-h
Base field 4.4.8000.1
Weight $[2, 2, 2, 2]$
Level norm $44$
Level $[44, 22, -w^{2} + w + 6]$
Dimension $4$
CM no
Base change no

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Base field 4.4.8000.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[44, 22, -w^{2} + w + 6]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ $\phantom{-}1$
5 $[5, 5, w^{2} - w - 5]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ $-2e^{3} - 8e^{2} + 5$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $\phantom{-}e^{3} + 3e^{2} - 3e - 2$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $-1$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ $-e^{3} - 4e^{2} - 2e - 1$
29 $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ $\phantom{-}3e^{3} + 13e^{2} + 7e - 6$
29 $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ $\phantom{-}3e^{3} + 13e^{2} + 2e - 11$
29 $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ $-2e^{3} - 6e^{2} + 6e + 5$
29 $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ $\phantom{-}e^{3} + 2e^{2} - 6e - 5$
41 $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ $-2e^{3} - 11e^{2} - 11e + 2$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ $-e^{3} - 5e^{2} - 2e + 2$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ $\phantom{-}e^{3} + 4e^{2} - 3e - 4$
41 $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ $\phantom{-}2e^{3} + 11e^{2} + 11e - 7$
79 $[79, 79, -w^{3} - w^{2} + 4w - 1]$ $-3e^{2} - 9e - 6$
79 $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ $\phantom{-}3e^{2} + 7e - 2$
79 $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ $\phantom{-}3e^{3} + 14e^{2} + 11e - 12$
79 $[79, 79, w^{3} - w^{2} - 6w + 9]$ $\phantom{-}2e^{3} + 10e^{2} + 11e - 5$
81 $[81, 3, -3]$ $-3e^{3} - 11e^{2} + 4e + 15$
109 $[109, 109, w^{2} - w - 7]$ $-4e^{3} - 14e^{2} - e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ $-1$
$11$ $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $1$