Properties

Label 3.3.564.1-12.1-b
Base field 3.3.564.1
Weight $[2, 2, 2]$
Level norm $12$
Level $[12, 6, w^{2} - 3]$
Dimension $1$
CM no
Base change no

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Base field 3.3.564.1

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

Form

Weight: $[2, 2, 2]$
Level: $[12, 6, w^{2} - 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w - 2]$ $-2$
13 $[13, 13, w^{2} - 2w - 2]$ $-4$
17 $[17, 17, -w^{2} + 2]$ $-6$
19 $[19, 19, -w^{2} + w + 1]$ $-4$
31 $[31, 31, -w + 4]$ $-10$
41 $[41, 41, -w^{2} + 2w - 2]$ $\phantom{-}6$
41 $[41, 41, -2w^{2} - 3w + 4]$ $\phantom{-}6$
41 $[41, 41, 2w + 1]$ $\phantom{-}6$
43 $[43, 43, -w^{2} - w + 5]$ $\phantom{-}2$
47 $[47, 47, -w^{2} + 8]$ $-12$
47 $[47, 47, 2w^{2} - w - 8]$ $-12$
53 $[53, 53, w^{2} + w - 7]$ $-6$
59 $[59, 59, w^{2} - 2w - 4]$ $\phantom{-}0$
61 $[61, 61, -3w^{2} + 14]$ $\phantom{-}2$
61 $[61, 61, 4w^{2} - 2w - 19]$ $-4$
61 $[61, 61, -2w^{2} + 7]$ $\phantom{-}8$
67 $[67, 67, -2w^{2} - w + 8]$ $-10$
71 $[71, 71, w^{2} + 2w - 4]$ $\phantom{-}12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w - 1]$ $-1$
$3$ $[3, 3, w]$ $-1$