Properties

Label 3.3.1573.1-8.2-b
Base field 3.3.1573.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 8, w - 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1573.1

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

Form

Weight: $[2, 2, 2]$
Level: $[8, 8, w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

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 $[2, 2, -w]$ $\phantom{-}0$
4 $[4, 2, w^{2} - w - 7]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}e - 4$
7 $[7, 7, w + 1]$ $\phantom{-}2e - 2$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}0$
13 $[13, 13, w + 3]$ $\phantom{-}2e - 5$
13 $[13, 13, -2w + 1]$ $-2e - 1$
19 $[19, 19, 2w^{2} - w - 15]$ $-4e + 2$
25 $[25, 5, w^{2} - 7]$ $\phantom{-}e - 6$
27 $[27, 3, 3]$ $-2e + 8$
31 $[31, 31, w^{2} - 2w - 1]$ $-2e + 6$
37 $[37, 37, -3w^{2} + 2w + 23]$ $-3e$
41 $[41, 41, -2w - 1]$ $-5e + 6$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}2e - 2$
49 $[49, 7, w^{2} - 2w - 5]$ $-2e - 6$
59 $[59, 59, 2w - 3]$ $-4$
67 $[67, 67, w - 5]$ $\phantom{-}2e + 8$
71 $[71, 71, w^{2} - 2w - 11]$ $-4e + 10$
73 $[73, 73, w^{2} + 1]$ $\phantom{-}4e - 14$
83 $[83, 83, -4w^{2} + 3w + 27]$ $-2e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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