Properties

Label 3.3.316.1-32.1-a
Base field 3.3.316.1
Weight $[2, 2, 2]$
Level norm $32$
Level $[32, 4, 2w^{2} - 8]$
Dimension $1$
CM no
Base change no

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Base field 3.3.316.1

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

Form

Weight: $[2, 2, 2]$
Level: $[32, 4, 2w^{2} - 8]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}0$
2 $[2, 2, w - 1]$ $-1$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}4$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}6$
19 $[19, 19, w^{2} - w + 1]$ $\phantom{-}4$
23 $[23, 23, 2w - 3]$ $\phantom{-}8$
27 $[27, 3, 3]$ $-4$
29 $[29, 29, 2w + 1]$ $\phantom{-}2$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}0$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-6$
41 $[41, 41, 2w^{2} - 9]$ $\phantom{-}2$
43 $[43, 43, w^{2} + w - 5]$ $\phantom{-}4$
43 $[43, 43, -3w^{2} + w + 15]$ $-4$
43 $[43, 43, -2w^{2} + 2w + 11]$ $-12$
53 $[53, 53, w^{2} - w - 7]$ $-6$
61 $[61, 61, 4w^{2} - 2w - 15]$ $-14$
67 $[67, 67, -5w^{2} + 3w + 23]$ $\phantom{-}12$
73 $[73, 73, 2w^{2} - 3]$ $-2$
73 $[73, 73, -3w^{2} - w + 7]$ $-14$
73 $[73, 73, -6w^{2} + 4w + 25]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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