Properties

Label 3.3.568.1-20.1-d
Base field 3.3.568.1
Weight $[2, 2, 2]$
Level norm $20$
Level $[20, 10, -w^{2} + w + 2]$
Dimension $1$
CM no
Base change no

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Base field 3.3.568.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[20, 10, -w^{2} + w + 2]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
2 $[2, 2, w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{2} - w - 7]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}2$
17 $[17, 17, -w^{2} + w + 3]$ $-2$
25 $[25, 5, -w^{2} - w - 1]$ $-4$
27 $[27, 3, 3]$ $-2$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}0$
37 $[37, 37, 3w^{2} - 5w - 13]$ $-2$
41 $[41, 41, 2w - 1]$ $\phantom{-}2$
53 $[53, 53, 5w^{2} - 9w - 21]$ $\phantom{-}4$
53 $[53, 53, 3w^{2} - 5w - 15]$ $-6$
53 $[53, 53, w^{2} - 3w - 7]$ $\phantom{-}4$
59 $[59, 59, w^{2} - 3w - 5]$ $\phantom{-}0$
61 $[61, 61, 2w^{2} - 4w - 9]$ $-8$
61 $[61, 61, 2w - 7]$ $\phantom{-}2$
61 $[61, 61, 2w - 5]$ $\phantom{-}2$
67 $[67, 67, -w^{2} + w - 1]$ $-12$
71 $[71, 71, -2w - 5]$ $\phantom{-}2$
71 $[71, 71, 3w^{2} - 3w - 19]$ $\phantom{-}12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$2$ $[2, 2, w + 1]$ $-1$
$5$ $[5, 5, w^{2} - w - 7]$ $-1$