# Properties

 Label 5.5.14641.1-67.4-a Base field $$\Q(\zeta_{11})^+$$ Weight $[2, 2, 2, 2, 2]$ Level norm $67$ Level $[67,67,w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## 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: $[67,67,w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $2$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{2} - 24$$
Norm Prime Eigenvalue
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}e$
23 $[23, 23, -w^{4} + 3w^{2} + 1]$ $-e + 1$
23 $[23, 23, -w^{4} + 3w^{2} + w - 2]$ $-\frac{1}{2}e - 5$
23 $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ $\phantom{-}\frac{1}{2}e + 3$
23 $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}e + 2$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}4$
32 $[32, 2, 2]$ $-\frac{1}{2}e - 1$
43 $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ $\phantom{-}4$
43 $[43, 43, -w^{4} + 2w^{2} + w + 1]$ $\phantom{-}9$
43 $[43, 43, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}4$
43 $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ $-2e - 2$
43 $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ $\phantom{-}e - 3$
67 $[67, 67, 2w^{4} - 7w^{2} + 2]$ $-2e - 3$
67 $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ $-2e + 2$
67 $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ $-2$
67 $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $\phantom{-}1$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}e - 4$
89 $[89, 89, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}e - 12$
89 $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $\phantom{-}e + 8$
89 $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ $-e - 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$67$ $[67,67,w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $-1$