# Properties

 Label 4.4.19525.1-19.2-b Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.19525.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 14x^{2} + 15x + 45$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $40$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}0$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $-2$
9 $[9, 3, -w + 3]$ $\phantom{-}2$
9 $[9, 3, w + 2]$ $\phantom{-}6$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $\phantom{-}2$
16 $[16, 2, 2]$ $-5$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}6$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-1$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $\phantom{-}0$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}0$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}8$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $\phantom{-}10$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $-8$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $-2$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $-4$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $\phantom{-}4$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $-6$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $\phantom{-}12$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $-10$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $-6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ $1$