Properties

Label 3.3.564.1-18.2-e
Base field 3.3.564.1
Weight $[2, 2, 2]$
Level norm $18$
Level $[18, 6, w^{2} - w - 2]$
Dimension $2$
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: $[18, 6, w^{2} - w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 3x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $-1$
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w - 2]$ $\phantom{-}0$
13 $[13, 13, w^{2} - 2w - 2]$ $\phantom{-}2e - 6$
17 $[17, 17, -w^{2} + 2]$ $-3e + 6$
19 $[19, 19, -w^{2} + w + 1]$ $-e + 3$
31 $[31, 31, -w + 4]$ $-4e + 6$
41 $[41, 41, -w^{2} + 2w - 2]$ $\phantom{-}3e - 3$
41 $[41, 41, -2w^{2} - 3w + 4]$ $\phantom{-}3e - 3$
41 $[41, 41, 2w + 1]$ $-3e$
43 $[43, 43, -w^{2} - w + 5]$ $-e + 6$
47 $[47, 47, -w^{2} + 8]$ $-6$
47 $[47, 47, 2w^{2} - w - 8]$ $\phantom{-}6$
53 $[53, 53, w^{2} + w - 7]$ $\phantom{-}0$
59 $[59, 59, w^{2} - 2w - 4]$ $\phantom{-}3e - 9$
61 $[61, 61, -3w^{2} + 14]$ $\phantom{-}2e$
61 $[61, 61, 4w^{2} - 2w - 19]$ $\phantom{-}8$
61 $[61, 61, -2w^{2} + 7]$ $\phantom{-}2e$
67 $[67, 67, -2w^{2} - w + 8]$ $-3e + 2$
71 $[71, 71, w^{2} + 2w - 4]$ $-6e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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