# Properties

 Base field 4.4.8789.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, w^{2} - w - 2]$ Label 4.4.8789.1-19.1-c Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

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

## Form

 Weight [2, 2, 2, 2] Level $[19, 19, w^{2} - w - 2]$ Label 4.4.8789.1-19.1-c Dimension 4 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} + 2x^{3} - 7x^{2} - 11x + 5$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}e + 2$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $-e^{3} - e^{2} + 6e + 3$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-e^{3} + 6e - 1$
16 $[16, 2, 2]$ $-3$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-e^{3} + 8e + 1$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-e^{3} + 7e + 2$
17 $[17, 17, -w^{2} + 2w + 1]$ $-2e$
19 $[19, 19, w^{2} - w - 2]$ $-1$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}0$
29 $[29, 29, w^{2} - w - 3]$ $-e^{3} - 2e^{2} + 5e + 8$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-e^{3} + e^{2} + 7e - 5$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-e^{3} + 7e - 2$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}e^{3} - e^{2} - 7e + 5$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}2e + 2$
61 $[61, 61, -w - 3]$ $\phantom{-}e^{3} - e^{2} - 8e + 5$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}2e^{2} - 2e - 6$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}e^{3} - 3e^{2} - 7e + 13$
81 $[81, 3, -3]$ $\phantom{-}3e^{3} + 3e^{2} - 15e - 9$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}e^{3} + e^{2} - 6e - 7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, w^{2} - w - 2]$ $1$