Properties

Label 3.3.1436.1-12.3-b
Base field 3.3.1436.1
Weight $[2, 2, 2]$
Level norm $12$
Level $[12, 12, w]$
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: $[12, 12, w]$
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:

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 9]$ $\phantom{-}1$
9 $[9, 3, -w^{2} + 3w + 5]$ $-e - 2$
11 $[11, 11, -w^{2} + w + 11]$ $\phantom{-}e + 2$
13 $[13, 13, 2w^{2} - 4w - 13]$ $-3e - 2$
23 $[23, 23, -w^{2} + w + 7]$ $-2e - 7$
29 $[29, 29, -w^{2} - w + 1]$ $\phantom{-}2e + 1$
41 $[41, 41, -2w^{2} + 2w + 19]$ $\phantom{-}4e$
41 $[41, 41, w^{2} - 3w - 7]$ $\phantom{-}3e - 1$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}2e - 2$
47 $[47, 47, 3w^{2} - 7w - 17]$ $\phantom{-}2e - 2$
53 $[53, 53, -2w - 1]$ $-6e - 5$
61 $[61, 61, -2w + 7]$ $\phantom{-}7e - 1$
67 $[67, 67, 3w^{2} - 5w - 23]$ $\phantom{-}e - 8$
67 $[67, 67, 2w^{2} - 4w - 11]$ $\phantom{-}2e - 3$
67 $[67, 67, 3w^{2} - 7w - 13]$ $-2e + 5$
79 $[79, 79, w^{2} + w - 5]$ $\phantom{-}9e + 1$
89 $[89, 89, 5w^{2} - 7w - 47]$ $\phantom{-}12e + 5$
97 $[97, 97, 5w^{2} - 11w - 29]$ $\phantom{-}e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w - 2]$ $-1$
$3$ $[3, 3, w^{2} - w - 9]$ $-1$