# Properties

 Label 4.4.12400.1-19.1-a Base field 4.4.12400.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.12400.1

Generator $$w$$, with minimal polynomial $$x^{4} - 12x^{2} + 31$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ $-2$
5 $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ $\phantom{-}0$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ $-4$
9 $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ $\phantom{-}2$
19 $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ $-4$
29 $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ $\phantom{-}6$
29 $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ $\phantom{-}6$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-8$
59 $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ $\phantom{-}6$
59 $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ $\phantom{-}0$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ $\phantom{-}2$
61 $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ $\phantom{-}8$
71 $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ $\phantom{-}0$
71 $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ $-12$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ $\phantom{-}16$
79 $[79, 79, -2w^{2} + w + 10]$ $\phantom{-}10$
79 $[79, 79, 2w^{2} + w - 10]$ $-8$
79 $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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