# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} - w + 4]$ Label 3.3.1129.1-19.1-a Dimension 1 CM no Base change no

# Learn more about

## Base field 3.3.1129.1

Generator $$w$$, with minimal polynomial $$x^{3} - 7x - 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[19, 19, -w^{2} - w + 4]$ Label 3.3.1129.1-19.1-a Dimension 1 Is CM no Is base change no Parent newspace dimension 36

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w + 1]$ $\phantom{-}2$
3 $[3, 3, w + 2]$ $\phantom{-}1$
8 $[8, 2, 2]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + 5]$ $-3$
13 $[13, 13, w^{2} - w - 7]$ $-1$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}6$
19 $[19, 19, -w^{2} - w + 4]$ $-1$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-9$
31 $[31, 31, w^{2} - 2w - 4]$ $\phantom{-}4$
37 $[37, 37, -2w^{2} + 3w + 7]$ $\phantom{-}4$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}3$
59 $[59, 59, 2w^{2} - 13]$ $-6$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}4$
67 $[67, 67, 2w^{2} - w - 11]$ $-10$
73 $[73, 73, -w^{2} - 1]$ $-2$
83 $[83, 83, w^{2} - w - 10]$ $-12$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}6$
97 $[97, 97, w^{2} - 2w - 7]$ $-2$
97 $[97, 97, -w^{2} - 4w - 5]$ $\phantom{-}8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} - w + 4]$ $1$