# Properties

 Label 4.4.17600.1-19.3-b Base field 4.4.17600.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,-\frac{1}{2}w^{3} + w^{2} + 4w - 9]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.17600.1

Generator $$w$$, with minimal polynomial $$x^{4} - 14x^{2} + 44$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19,19,-\frac{1}{2}w^{3} + w^{2} + 4w - 9]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $34$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $-2$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $\phantom{-}0$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $-6$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $\phantom{-}2$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $\phantom{-}6$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $-4$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $-1$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $\phantom{-}6$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $\phantom{-}10$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $\phantom{-}10$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $-6$
31 $[31, 31, -w - 1]$ $\phantom{-}8$
31 $[31, 31, w - 1]$ $-8$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $-6$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $\phantom{-}10$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $-2$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $-2$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $\phantom{-}12$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $-4$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $\phantom{-}8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-\frac{1}{2}w^{3} + w^{2} + 4w - 9]$ $1$