Properties

Label 4.4.6809.1-11.1-a
Base field 4.4.6809.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, w^{3} - 5w + 1]$
Dimension $2$
CM no
Base change no

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Base field 4.4.6809.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, w^{3} - 5w + 1]$
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:

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 4w]$ $-e - 3$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $\phantom{-}e + 2$
11 $[11, 11, w^{3} - 5w + 1]$ $\phantom{-}1$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $\phantom{-}2e - 4$
23 $[23, 23, -w^{2} + 2]$ $-3e - 2$
29 $[29, 29, -w^{2} - w + 3]$ $-e - 5$
31 $[31, 31, -w^{3} + 6w + 2]$ $\phantom{-}6e - 1$
43 $[43, 43, w^{3} - 6w]$ $-2e - 2$
47 $[47, 47, 2w^{3} - 9w]$ $-4e - 5$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $\phantom{-}7$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $-8e - 3$
59 $[59, 59, w^{2} - w - 5]$ $-9e - 7$
59 $[59, 59, 3w^{3} - 15w - 5]$ $-9e - 7$
71 $[71, 71, w^{3} - 3w - 3]$ $\phantom{-}14e + 7$
81 $[81, 3, -3]$ $\phantom{-}4e - 11$
83 $[83, 83, -2w^{3} + 8w + 3]$ $-3e + 7$
89 $[89, 89, -2w^{3} + 11w - 2]$ $-2e - 1$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $-16$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $-3e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w^{3} - 5w + 1]$ $-1$