# Properties

 Base field 4.4.8789.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11, 11, -w^{3} + 2w^{2} + 4w]$ Label 4.4.8789.1-11.1-a 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 $[11, 11, -w^{3} + 2w^{2} + 4w]$ Label 4.4.8789.1-11.1-a Dimension 4 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 7x^{2} - 6x - 1$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}2e^{3} - e^{2} - 12e - 6$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $-1$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-2e^{3} + 16e + 10$
16 $[16, 2, 2]$ $\phantom{-}e^{3} - 8e - 2$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}2e^{3} - 2e^{2} - 13e$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}2e^{3} - 14e - 8$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}4e^{3} - 2e^{2} - 26e - 10$
19 $[19, 19, w^{2} - w - 2]$ $-4e^{3} + 3e^{2} + 24e + 6$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-3e^{3} + 23e + 12$
29 $[29, 29, w^{2} - w - 3]$ $-e^{2} + 1$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-2e^{3} - e^{2} + 14e + 13$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-2e^{2} + 2e + 10$
47 $[47, 47, w^{3} - 7w - 4]$ $-e^{2} + 2e + 3$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}2e^{3} - e^{2} - 10e - 7$
61 $[61, 61, -w - 3]$ $-e^{3} + 2e^{2} + 5e + 4$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}4e^{3} - 4e^{2} - 26e - 4$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}5e^{3} - 39e - 22$
81 $[81, 3, -3]$ $-6e^{3} + 4e^{2} + 38e + 20$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-10e^{3} + 4e^{2} + 66e + 26$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $1$