Properties

Label 3.3.1016.1-6.2-b
Base field 3.3.1016.1
Weight $[2, 2, 2]$
Level norm $6$
Level $[6, 6, w - 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1016.1

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

Form

Weight: $[2, 2, 2]$
Level: $[6, 6, w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
2 $[2, 2, w - 3]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 5]$ $-1$
9 $[9, 3, w^{2} + w - 1]$ $\phantom{-}e - 3$
13 $[13, 13, 2w^{2} - 2w - 11]$ $\phantom{-}e + 1$
29 $[29, 29, -w^{2} - 3w - 1]$ $-2$
29 $[29, 29, -w^{2} + w + 3]$ $-e - 1$
29 $[29, 29, 2w - 5]$ $-4e + 2$
31 $[31, 31, -w^{2} + w + 1]$ $-4$
37 $[37, 37, -2w - 1]$ $-2e$
43 $[43, 43, -2w - 3]$ $\phantom{-}2e - 6$
47 $[47, 47, 2w - 3]$ $\phantom{-}e + 3$
59 $[59, 59, 4w^{2} + 8w - 1]$ $-3e - 1$
61 $[61, 61, -w^{2} - w - 1]$ $-2e$
67 $[67, 67, w^{2} + w - 5]$ $-4e + 4$
71 $[71, 71, w^{2} - w - 9]$ $-4e + 4$
73 $[73, 73, -2w^{2} + 2w + 9]$ $\phantom{-}2e + 4$
73 $[73, 73, 6w^{2} + 10w - 7]$ $\phantom{-}5e - 7$
73 $[73, 73, 3w^{2} - 3w - 17]$ $-2e + 12$
79 $[79, 79, -2w^{2} + 2w + 15]$ $\phantom{-}2e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$3$ $[3, 3, w^{2} - w - 5]$ $1$