Properties

Label 4.4.8112.1-1.1-a
Base field 4.4.8112.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $4$
CM no
Base change yes

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Base field 4.4.8112.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
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:

\(x^{4} - 13x^{2} + 24\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, w^{2} - w - 1]$ $-e$
9 $[9, 3, -w^{2} + 2]$ $-e^{2} + 8$
13 $[13, 13, w^{3} - 4w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$
13 $[13, 13, -w^{3} + 4w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$
17 $[17, 17, w^{3} - 3w - 1]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
17 $[17, 17, -w^{3} + 3w - 1]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
29 $[29, 29, w^{3} + w^{2} - 4w - 2]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e$
43 $[43, 43, w^{2} + w - 4]$ $\phantom{-}e^{2} - 8$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}e^{2} - 8$
53 $[53, 53, w^{3} - 2w - 2]$ $\phantom{-}0$
53 $[53, 53, -w^{3} + 2w - 2]$ $\phantom{-}0$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-e^{3} + 9e$
79 $[79, 79, -w^{3} - w^{2} + 4w + 1]$ $-e^{3} + 9e$
101 $[101, 101, -w^{3} + w^{2} + 3w - 5]$ $-6$
101 $[101, 101, w^{3} + w^{2} - 3w - 5]$ $-6$
103 $[103, 103, 2w^{2} - w - 4]$ $-4$
103 $[103, 103, 2w^{2} + w - 4]$ $-4$
107 $[107, 107, 2w^{2} + w - 5]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).