Properties

Base field \(\Q(\zeta_{11})^+\)
Weight [2, 2, 2, 2, 2]
Level norm 32
Level $[32, 2, 2]$
Label 5.5.14641.1-32.1-a
Dimension 2
CM no
Base change yes

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Base field \(\Q(\zeta_{11})^+\)

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2]
Level $[32, 2, 2]$
Label 5.5.14641.1-32.1-a
Dimension 2
Is CM no
Is base change yes
Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut x \) \(\mathstrut -\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}e$
23 $[23, 23, -w^{4} + 3w^{2} + 1]$ $\phantom{-}2e$
23 $[23, 23, -w^{4} + 3w^{2} + w - 2]$ $\phantom{-}2e$
23 $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ $\phantom{-}2e$
23 $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}2e$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}2e$
32 $[32, 2, 2]$ $\phantom{-}1$
43 $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ $-9e - 3$
43 $[43, 43, -w^{4} + 2w^{2} + w + 1]$ $-9e - 3$
43 $[43, 43, w^{3} + w^{2} - 4w - 2]$ $-9e - 3$
43 $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ $-9e - 3$
43 $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ $-9e - 3$
67 $[67, 67, 2w^{4} - 7w^{2} + 2]$ $\phantom{-}5e + 8$
67 $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ $\phantom{-}5e + 8$
67 $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ $\phantom{-}5e + 8$
67 $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $\phantom{-}5e + 8$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}5e + 8$
89 $[89, 89, w^{3} + w^{2} - 4w - 1]$ $-5e - 5$
89 $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $-5e - 5$
89 $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ $-5e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
32 $[32, 2, 2]$ $-1$