Properties

Label 4.4.10304.1-8.4-a
Base field 4.4.10304.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8,4,\frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$
Dimension $2$
CM no
Base change no

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Base field 4.4.10304.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 8\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8,4,\frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 2]$ $\phantom{-}e$
2 $[2, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 1]$ $\phantom{-}0$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + w - 3]$ $\phantom{-}2$
23 $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ $\phantom{-}2e$
25 $[25, 5, -\frac{1}{2}w^{3} + \frac{9}{2}w + 1]$ $-2e$
25 $[25, 5, -\frac{1}{2}w^{3} + \frac{5}{2}w - 1]$ $\phantom{-}2e + 4$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 1]$ $\phantom{-}6$
31 $[31, 31, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w + 1]$ $-4e + 2$
41 $[41, 41, \frac{3}{2}w^{3} - w^{2} - \frac{21}{2}w - 5]$ $-2e + 2$
41 $[41, 41, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 7]$ $-2e + 2$
47 $[47, 47, -w^{2} - w + 5]$ $-2e + 4$
47 $[47, 47, -w^{3} + \frac{1}{2}w^{2} + \frac{13}{2}w + 5]$ $-6e + 8$
49 $[49, 7, \frac{1}{2}w^{2} - \frac{1}{2}w - 5]$ $\phantom{-}2e - 2$
73 $[73, 73, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $-6e + 6$
73 $[73, 73, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 1]$ $\phantom{-}10e - 10$
79 $[79, 79, w^{2} - 3w + 1]$ $\phantom{-}4e + 2$
79 $[79, 79, w^{2} + w - 1]$ $\phantom{-}4e + 2$
81 $[81, 3, -3]$ $-6e + 2$
89 $[89, 89, -\frac{1}{2}w^{3} + 3w^{2} + \frac{7}{2}w - 11]$ $-2e + 14$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{5}{2}w - 3]$ $-4e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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