Properties

Label 3.3.568.1-22.2-e
Base field 3.3.568.1
Weight $[2, 2, 2]$
Level norm $22$
Level $[22, 22, w - 4]$
Dimension $2$
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: $[22, 22, w - 4]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
2 $[2, 2, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{2} - w - 7]$ $\phantom{-}e + 2$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}1$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}3e + 3$
25 $[25, 5, -w^{2} - w - 1]$ $\phantom{-}5$
27 $[27, 3, 3]$ $\phantom{-}e$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}e - 2$
37 $[37, 37, 3w^{2} - 5w - 13]$ $-7e - 2$
41 $[41, 41, 2w - 1]$ $-3e$
53 $[53, 53, 5w^{2} - 9w - 21]$ $-2e$
53 $[53, 53, 3w^{2} - 5w - 15]$ $\phantom{-}5e + 5$
53 $[53, 53, w^{2} - 3w - 7]$ $\phantom{-}2e + 3$
59 $[59, 59, w^{2} - 3w - 5]$ $-4e - 6$
61 $[61, 61, 2w^{2} - 4w - 9]$ $\phantom{-}3e - 1$
61 $[61, 61, 2w - 7]$ $-3e + 10$
61 $[61, 61, 2w - 5]$ $\phantom{-}4e - 4$
67 $[67, 67, -w^{2} + w - 1]$ $-5e + 4$
71 $[71, 71, -2w - 5]$ $-e + 11$
71 $[71, 71, 3w^{2} - 3w - 19]$ $\phantom{-}5e + 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$
$11$ $[11, 11, -w^{2} + w + 1]$ $-1$