Properties

Label 4.4.13824.1-22.1-a
Base field 4.4.13824.1
Weight $[2, 2, 2, 2]$
Level norm $22$
Level $[22, 22, -w^{3} + w^{2} + 3w - 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.13824.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 6\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[22, 22, -w^{3} + w^{2} + 3w - 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 6x^{3} - 6x^{2} + 45x + 27\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}1$
3 $[3, 3, w^{2} - w - 3]$ $\phantom{-}\frac{1}{3}e^{2} - e - 3$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}e$
11 $[11, 11, -w^{2} - w + 1]$ $-1$
13 $[13, 13, w^{3} - 4w + 1]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{1}{3}e^{2} - \frac{5}{3}e$
13 $[13, 13, -w^{3} + 4w + 1]$ $-\frac{2}{9}e^{3} + \frac{2}{3}e^{2} + \frac{7}{3}e - 3$
25 $[25, 5, -w^{2} - 2w + 1]$ $-\frac{2}{9}e^{3} + \frac{1}{3}e^{2} + \frac{13}{3}e$
25 $[25, 5, w^{2} - 2w - 1]$ $-\frac{2}{9}e^{3} + \frac{4}{3}e^{2} - \frac{2}{3}e - 9$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}\frac{4}{9}e^{3} - \frac{7}{3}e^{2} - \frac{5}{3}e + 6$
37 $[37, 37, w^{3} - 3w + 1]$ $-\frac{2}{9}e^{3} + e^{2} + \frac{4}{3}e - 6$
59 $[59, 59, w^{2} - w - 5]$ $-\frac{1}{3}e^{2} - e$
59 $[59, 59, -w^{2} - w + 5]$ $-e^{2} + e + 12$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $\phantom{-}\frac{1}{9}e^{3} - e^{2} - \frac{2}{3}e + 3$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $\phantom{-}\frac{1}{9}e^{3} + e^{2} - \frac{14}{3}e - 15$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}\frac{1}{3}e^{3} - 2e^{2} - 2e + 5$
73 $[73, 73, 2w - 1]$ $-\frac{2}{9}e^{3} + \frac{7}{3}e^{2} - \frac{8}{3}e - 15$
73 $[73, 73, -2w - 1]$ $\phantom{-}\frac{4}{9}e^{3} - \frac{5}{3}e^{2} - \frac{17}{3}e + 9$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}e^{3} - \frac{14}{3}e^{2} - 4e + 14$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $-\frac{1}{3}e^{2} - 2e + 6$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e^{2} + 3e + 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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