Properties

Label 4.4.13448.1-8.1-d
Base field 4.4.13448.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 2, -w^{3} + 7w]$
Dimension $2$
CM no
Base change no

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Base field 4.4.13448.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 2, -w^{3} + 7w]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
4 $[4, 2, -w + 1]$ $-1$
5 $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$ $\phantom{-}e$
5 $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ $-e - 1$
25 $[25, 5, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 4]$ $\phantom{-}4$
37 $[37, 37, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w]$ $-2e + 4$
37 $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w]$ $\phantom{-}2e + 6$
43 $[43, 43, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 2]$ $\phantom{-}e - 4$
43 $[43, 43, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + 10w + 2]$ $-e - 5$
49 $[49, 7, -w^{2} - w + 3]$ $\phantom{-}6$
49 $[49, 7, -w^{2} + w + 3]$ $\phantom{-}6$
59 $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 2]$ $\phantom{-}2e + 6$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 2]$ $-2e + 4$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 2]$ $-e + 7$
61 $[61, 61, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 8w - 4]$ $\phantom{-}e + 8$
73 $[73, 73, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 2w]$ $\phantom{-}0$
73 $[73, 73, w^{2} - w + 1]$ $-3e - 7$
73 $[73, 73, w^{2} + w + 1]$ $\phantom{-}3e - 4$
73 $[73, 73, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 2w]$ $\phantom{-}0$
81 $[81, 3, -3]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$
$4$ $[4, 2, -w + 1]$ $1$