# Properties

 Label 3.3.785.1-8.1-b Base field 3.3.785.1 Weight $[2, 2, 2]$ Level norm $8$ Level $[8, 2, 2]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.785.1

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

## Form

 Weight: $[2, 2, 2]$ Level: $[8, 2, 2]$ 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:

 $$x^{2} + 3x + 1$$
Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}2e + 2$
5 $[5, 5, -w + 3]$ $-2$
8 $[8, 2, 2]$ $-1$
9 $[9, 3, w^{2} + w - 4]$ $\phantom{-}e + 4$
13 $[13, 13, w + 3]$ $-2e - 4$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}3e + 5$
23 $[23, 23, w^{2} - 2]$ $-6e - 10$
23 $[23, 23, w^{2} - 3]$ $\phantom{-}4e + 2$
23 $[23, 23, -w^{2} + 8]$ $-6e - 10$
29 $[29, 29, w - 4]$ $-2e - 8$
37 $[37, 37, w^{2} + w - 8]$ $\phantom{-}2e$
41 $[41, 41, w^{2} + 2w - 4]$ $-e + 4$
47 $[47, 47, 2w^{2} + w - 8]$ $\phantom{-}2e + 6$
59 $[59, 59, -2w^{2} - 3w + 6]$ $-11e - 14$
61 $[61, 61, -2w - 1]$ $\phantom{-}8$
67 $[67, 67, -2w - 3]$ $\phantom{-}e - 3$
79 $[79, 79, 2w^{2} - 9]$ $-6e - 4$
109 $[109, 109, w^{2} + 2w - 6]$ $-4e - 16$
109 $[109, 109, 2w^{2} + w - 14]$ $-10e - 20$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$8$ $[8, 2, 2]$ $1$