# Properties

 Base field $$\Q(\zeta_{11})^+$$ Weight [2, 2, 2, 2, 2] Level norm 197 Level $[197, 197, 3w^{4} - w^{3} - 10w^{2} + w + 5]$ Label 5.5.14641.1-197.1-b Dimension 1 CM no Base change no

# Related objects

## 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 $[197, 197, 3w^{4} - w^{3} - 10w^{2} + w + 5]$ Label 5.5.14641.1-197.1-b Dimension 1 Is CM no Is base change no Parent newspace dimension 8

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $-1$
23 $[23, 23, -w^{4} + 3w^{2} + 1]$ $-5$
23 $[23, 23, -w^{4} + 3w^{2} + w - 2]$ $-4$
23 $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ $\phantom{-}1$
23 $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-9$
23 $[23, 23, -w^{2} + w + 3]$ $-9$
32 $[32, 2, 2]$ $-9$
43 $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ $-3$
43 $[43, 43, -w^{4} + 2w^{2} + w + 1]$ $\phantom{-}3$
43 $[43, 43, w^{3} + w^{2} - 4w - 2]$ $-11$
43 $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ $\phantom{-}10$
43 $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ $\phantom{-}7$
67 $[67, 67, 2w^{4} - 7w^{2} + 2]$ $-13$
67 $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ $-10$
67 $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ $\phantom{-}4$
67 $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $\phantom{-}6$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $-2$
89 $[89, 89, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}6$
89 $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $-6$
89 $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ $\phantom{-}15$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
197 $[197, 197, 3w^{4} - w^{3} - 10w^{2} + w + 5]$ $1$