Properties

Label 3.3.1436.1-8.2-b
Base field 3.3.1436.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 4, -w^{2} + w + 8]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1436.1

Generator \(w\), with minimal polynomial \(x^{3} - 11x - 12\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 4, -w^{2} + w + 8]$
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:

\(x^{2} + x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}1$
3 $[3, 3, w^{2} - w - 9]$ $\phantom{-}e$
9 $[9, 3, -w^{2} + 3w + 5]$ $-e - 2$
11 $[11, 11, -w^{2} + w + 11]$ $-2e + 1$
13 $[13, 13, 2w^{2} - 4w - 13]$ $\phantom{-}e - 4$
23 $[23, 23, -w^{2} + w + 7]$ $-3$
29 $[29, 29, -w^{2} - w + 1]$ $-2e - 5$
41 $[41, 41, -2w^{2} + 2w + 19]$ $\phantom{-}2e - 7$
41 $[41, 41, w^{2} - 3w - 7]$ $\phantom{-}4e + 1$
41 $[41, 41, w^{2} - w - 5]$ $-5e - 5$
47 $[47, 47, 3w^{2} - 7w - 17]$ $\phantom{-}e - 5$
53 $[53, 53, -2w - 1]$ $\phantom{-}2e - 1$
61 $[61, 61, -2w + 7]$ $\phantom{-}4e - 1$
67 $[67, 67, 3w^{2} - 5w - 23]$ $\phantom{-}2e + 3$
67 $[67, 67, 2w^{2} - 4w - 11]$ $\phantom{-}2e - 9$
67 $[67, 67, 3w^{2} - 7w - 13]$ $\phantom{-}2e - 5$
79 $[79, 79, w^{2} + w - 5]$ $-e$
89 $[89, 89, 5w^{2} - 7w - 47]$ $-12$
97 $[97, 97, 5w^{2} - 11w - 29]$ $\phantom{-}3e + 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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