Properties

Label 3.3.469.1-32.1-b
Base field 3.3.469.1
Weight $[2, 2, 2]$
Level norm $32$
Level $[32, 4, -2w^{2} - 2w + 6]$
Dimension $2$
CM no
Base change no

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Base field 3.3.469.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[32, 4, -2w^{2} - 2w + 6]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 6x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $-1$
4 $[4, 2, -w^{2} - w + 3]$ $\phantom{-}0$
7 $[7, 7, w + 1]$ $\phantom{-}e$
7 $[7, 7, -w + 3]$ $\phantom{-}2$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}2e + 6$
17 $[17, 17, w + 3]$ $\phantom{-}4$
19 $[19, 19, w^{2} - 7]$ $-2e - 4$
27 $[27, 3, 3]$ $\phantom{-}e + 2$
43 $[43, 43, -2w - 5]$ $\phantom{-}5e + 16$
47 $[47, 47, 2w + 3]$ $\phantom{-}e - 2$
53 $[53, 53, 3w^{2} + 2w - 9]$ $-3e - 2$
59 $[59, 59, 2w^{2} + w - 5]$ $\phantom{-}4$
61 $[61, 61, 3w - 1]$ $-2e - 6$
61 $[61, 61, 2w^{2} + w - 9]$ $\phantom{-}2e + 10$
61 $[61, 61, 2w^{2} - w - 7]$ $-2e - 8$
67 $[67, 67, -2w^{2} + 13]$ $-2e - 4$
67 $[67, 67, -3w - 7]$ $-e + 6$
73 $[73, 73, w^{2} + 2w - 5]$ $\phantom{-}10$
79 $[79, 79, w - 5]$ $-4$
83 $[83, 83, -2w^{2} + 4w + 3]$ $\phantom{-}6e + 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 2]$ $1$
$4$ $[4, 2, -w^{2} - w + 3]$ $-1$