# Properties

 Label 6.6.1541581.1-11.2-c Base field 6.6.1541581.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $11$ Level $[11, 11, w^{2} - w - 2]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

# Learn more

## Base field 6.6.1541581.1

Generator $$w$$, with minimal polynomial $$x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[11, 11, w^{2} - w - 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + x - 3$$
Norm Prime Eigenvalue
5 $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ $\phantom{-}e$
11 $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ $-e$
11 $[11, 11, w^{2} - w - 2]$ $\phantom{-}1$
17 $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ $\phantom{-}e - 3$
27 $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ $\phantom{-}2$
27 $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-2e - 4$
37 $[37, 37, -w^{2} + 2w + 2]$ $-2e - 8$
47 $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ $-e$
53 $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ $-2e$
59 $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ $-e - 3$
64 $[64, 2, -2]$ $-8$
67 $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ $\phantom{-}5e - 2$
67 $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ $-3e + 1$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $-3e - 9$
71 $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $\phantom{-}6$
73 $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ $-e + 1$
83 $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ $-6e$
83 $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ $\phantom{-}6e$
89 $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ $-2e$
97 $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ $\phantom{-}2e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w^{2} - w - 2]$ $-1$