Properties

Label 3.3.1436.1-8.4-b
Base field 3.3.1436.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 8, -w + 4]$
Dimension $4$
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: $[8, 8, -w + 4]$
Dimension: $4$
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:

\(x^{4} - 5x^{2} + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 9]$ $\phantom{-}e$
9 $[9, 3, -w^{2} + 3w + 5]$ $-e^{3} + 4e$
11 $[11, 11, -w^{2} + w + 11]$ $\phantom{-}e^{2}$
13 $[13, 13, 2w^{2} - 4w - 13]$ $\phantom{-}e^{3} - 5e$
23 $[23, 23, -w^{2} + w + 7]$ $\phantom{-}e^{3} - 3e$
29 $[29, 29, -w^{2} - w + 1]$ $\phantom{-}4e$
41 $[41, 41, -2w^{2} + 2w + 19]$ $-2e^{3} + 9e$
41 $[41, 41, w^{2} - 3w - 7]$ $\phantom{-}3e^{2} - 4$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}0$
47 $[47, 47, 3w^{2} - 7w - 17]$ $-2e^{2} + 4$
53 $[53, 53, -2w - 1]$ $\phantom{-}3e^{3} - 13e$
61 $[61, 61, -2w + 7]$ $-e^{3} + 9e$
67 $[67, 67, 3w^{2} - 5w - 23]$ $-6e^{3} + 23e$
67 $[67, 67, 2w^{2} - 4w - 11]$ $-6e^{3} + 24e$
67 $[67, 67, 3w^{2} - 7w - 13]$ $\phantom{-}e^{2} - 2$
79 $[79, 79, w^{2} + w - 5]$ $\phantom{-}3e^{3} - 15e$
89 $[89, 89, 5w^{2} - 7w - 47]$ $-7e^{2} + 16$
97 $[97, 97, 5w^{2} - 11w - 29]$ $\phantom{-}5e^{3} - 26e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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