# Properties

 Base field $$\Q(\zeta_{11})^+$$ Weight [2, 2, 2, 2, 2] Level norm 43 Level $[43,43,-w^{4} + w^{3} + 4w^{2} - 4w - 2]$ Label 5.5.14641.1-43.5-a Dimension 1 CM no Base change no

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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 $[43,43,-w^{4} + w^{3} + 4w^{2} - 4w - 2]$ Label 5.5.14641.1-43.5-a Dimension 1 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}5$
23 $[23, 23, -w^{4} + 3w^{2} + 1]$ $\phantom{-}3$
23 $[23, 23, -w^{4} + 3w^{2} + w - 2]$ $\phantom{-}3$
23 $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ $-4$
23 $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-4$
23 $[23, 23, -w^{2} + w + 3]$ $-4$
32 $[32, 2, 2]$ $-9$
43 $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ $-12$
43 $[43, 43, -w^{4} + 2w^{2} + w + 1]$ $\phantom{-}9$
43 $[43, 43, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}9$
43 $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ $-5$
43 $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ $\phantom{-}1$
67 $[67, 67, 2w^{4} - 7w^{2} + 2]$ $\phantom{-}12$
67 $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ $\phantom{-}5$
67 $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ $-2$
67 $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $-2$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $-2$
89 $[89, 89, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}6$
89 $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $\phantom{-}13$
89 $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ $-1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
43 $[43,43,-w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-1$