# Properties

 Label 3.3.316.1-4.3-a Base field 3.3.316.1 Weight $[2, 2, 2]$ Level norm $4$ Level $[4, 4, w + 1]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 3.3.316.1

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

## Form

 Weight: $[2, 2, 2]$ Level: $[4, 4, w + 1]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $1$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}2$
2 $[2, 2, w - 1]$ $\phantom{-}0$
11 $[11, 11, w^{2} - w - 1]$ $-4$
17 $[17, 17, -w^{2} - w + 3]$ $-4$
19 $[19, 19, w^{2} - w + 1]$ $-8$
23 $[23, 23, 2w - 3]$ $\phantom{-}4$
27 $[27, 3, 3]$ $\phantom{-}8$
29 $[29, 29, 2w + 1]$ $\phantom{-}4$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}0$
37 $[37, 37, 2w^{2} - 2w - 5]$ $\phantom{-}0$
41 $[41, 41, 2w^{2} - 9]$ $\phantom{-}6$
43 $[43, 43, w^{2} + w - 5]$ $\phantom{-}0$
43 $[43, 43, -3w^{2} + w + 15]$ $\phantom{-}8$
43 $[43, 43, -2w^{2} + 2w + 11]$ $-4$
53 $[53, 53, w^{2} - w - 7]$ $-4$
61 $[61, 61, 4w^{2} - 2w - 15]$ $-8$
67 $[67, 67, -5w^{2} + 3w + 23]$ $\phantom{-}16$
73 $[73, 73, 2w^{2} - 3]$ $\phantom{-}12$
73 $[73, 73, -3w^{2} - w + 7]$ $-6$
73 $[73, 73, -6w^{2} + 4w + 25]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w - 1]$ $-1$