Properties

Label 3.3.316.1-34.2-b
Base field 3.3.316.1
Weight $[2, 2, 2]$
Level norm $34$
Level $[34, 34, -w + 4]$
Dimension $2$
CM no
Base change no

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Base field 3.3.316.1

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

Form

Weight: $[2, 2, 2]$
Level: $[34, 34, -w + 4]$
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:

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $-1$
2 $[2, 2, w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{2} - w - 1]$ $-3e + 5$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}1$
19 $[19, 19, w^{2} - w + 1]$ $-e + 7$
23 $[23, 23, 2w - 3]$ $-e + 3$
27 $[27, 3, 3]$ $-2$
29 $[29, 29, 2w + 1]$ $-2e + 8$
31 $[31, 31, 2w^{2} - 2w - 9]$ $-2e + 4$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-2e + 4$
41 $[41, 41, 2w^{2} - 9]$ $\phantom{-}6e - 10$
43 $[43, 43, w^{2} + w - 5]$ $\phantom{-}5e - 3$
43 $[43, 43, -3w^{2} + w + 15]$ $\phantom{-}5e - 5$
43 $[43, 43, -2w^{2} + 2w + 11]$ $\phantom{-}5e - 5$
53 $[53, 53, w^{2} - w - 7]$ $-2e + 2$
61 $[61, 61, 4w^{2} - 2w - 15]$ $-4e + 4$
67 $[67, 67, -5w^{2} + 3w + 23]$ $-2e - 6$
73 $[73, 73, 2w^{2} - 3]$ $-2e - 4$
73 $[73, 73, -3w^{2} - w + 7]$ $-2e - 4$
73 $[73, 73, -6w^{2} + 4w + 25]$ $-2e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $1$
$17$ $[17, 17, -w^{2} - w + 3]$ $-1$