# Properties

 Label 4.4.11324.1-19.1-b Base field 4.4.11324.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, -w^{3} + 3w - 1]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.11324.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19, 19, -w^{3} + 3w - 1]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $23$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $-2$
4 $[4, 2, -w^{3} + 4w + 1]$ $-3$
5 $[5, 5, w + 1]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + w^{2} + 3w - 1]$ $-1$
19 $[19, 19, -w^{3} + 3w - 1]$ $-1$
23 $[23, 23, -w + 3]$ $\phantom{-}0$
31 $[31, 31, -w^{2} - 2w + 1]$ $-6$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $-5$
43 $[43, 43, 2w - 1]$ $-2$
53 $[53, 53, -w - 3]$ $-1$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}5$
61 $[61, 61, w^{3} - 3w - 5]$ $\phantom{-}1$
67 $[67, 67, w^{3} + w^{2} - 5w - 1]$ $\phantom{-}0$
81 $[81, 3, -3]$ $-1$
83 $[83, 83, -w^{3} + 5w - 3]$ $-2$
89 $[89, 89, w^{2} + 1]$ $-6$
97 $[97, 97, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}7$
97 $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ $\phantom{-}17$
97 $[97, 97, w^{3} - 3w - 3]$ $-7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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