Properties

Label 3.3.169.1-65.3-c
Base field 3.3.169.1
Weight $[2, 2, 2]$
Level norm $65$
Level $[65,65,-w^{2} + w + 7]$
Dimension $2$
CM no
Base change no

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Base field 3.3.169.1

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

Form

Weight: $[2, 2, 2]$
Level: $[65,65,-w^{2} + w + 7]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $\phantom{-}e$
5 $[5, 5, -w^{2} + w + 2]$ $-1$
5 $[5, 5, -w + 1]$ $\phantom{-}0$
8 $[8, 2, 2]$ $\phantom{-}e + 3$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}1$
27 $[27, 3, 3]$ $-e + 4$
31 $[31, 31, -2w^{2} + 3w + 3]$ $-4e - 4$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}2e + 2$
31 $[31, 31, -w^{2} + 3w + 4]$ $-2e + 2$
47 $[47, 47, 2w - 3]$ $-6$
47 $[47, 47, 2w^{2} - 4w - 7]$ $\phantom{-}e + 6$
47 $[47, 47, 2w^{2} - 2w - 3]$ $-e - 6$
53 $[53, 53, 3w^{2} - 4w - 8]$ $-2e$
53 $[53, 53, 4w^{2} - 6w - 11]$ $-e + 6$
53 $[53, 53, 3w^{2} - 5w - 6]$ $\phantom{-}2e + 6$
73 $[73, 73, w^{2} - 4w - 4]$ $\phantom{-}3e - 4$
73 $[73, 73, 2w^{2} - w - 8]$ $\phantom{-}e + 8$
73 $[73, 73, 3w^{2} - 5w - 5]$ $-4e - 4$
79 $[79, 79, -3w^{2} + 5w + 4]$ $-e + 8$
79 $[79, 79, 2w^{2} - w - 9]$ $-2e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,w^{2} - w - 2]$ $1$
$13$ $[13,13,2w^{2} - 3w - 5]$ $-1$