# Properties

 Base field 4.4.19821.1 Weight [2, 2, 2, 2] Level norm 57 Level $[57, 57, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 1]$ Label 4.4.19821.1-57.1-b Dimension 1 CM no Base change no

# Related objects

## Base field 4.4.19821.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} + 6x + 3$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[57, 57, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 1]$ Label 4.4.19821.1-57.1-b Dimension 1 Is CM no Is base change no Parent newspace dimension 103

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ $\phantom{-}1$
9 $[9, 3, w + 1]$ $-4$
13 $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ $-7$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ $-1$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ $\phantom{-}1$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ $-1$
25 $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ $-7$
25 $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ $-6$
29 $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ $\phantom{-}5$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ $\phantom{-}6$
37 $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-11$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ $\phantom{-}6$
43 $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ $-11$
47 $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ $-3$
59 $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ $\phantom{-}9$
59 $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ $\phantom{-}12$
67 $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ $-9$
71 $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}15$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $1$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ $-1$