# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 7 Level $[7, 7, -w^{2} + 2]$ Label 4.4.16997.1-7.1-b Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16997.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[7, 7, -w^{2} + 2]$ Label 4.4.16997.1-7.1-b Dimension 3 Is CM no Is base change no Parent newspace dimension 9

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} - 2x^{2} - 8x - 4$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}e$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $-2e^{2} + 5e + 8$
13 $[13, 13, w^{2} - w - 4]$ $-2e^{2} + 6e + 10$
16 $[16, 2, 2]$ $\phantom{-}e^{2} - 4e - 5$
19 $[19, 19, -w^{2} + w + 1]$ $\phantom{-}2e^{2} - 6e - 12$
23 $[23, 23, -w^{3} + 4w + 2]$ $\phantom{-}2e^{2} - 7e - 10$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}2e^{2} - 7e - 10$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $-2e^{2} + 6e + 6$
29 $[29, 29, -w + 3]$ $-2$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}2e^{2} - 7e - 14$
37 $[37, 37, w^{3} - 4w - 1]$ $\phantom{-}e^{2} - 4e - 6$
37 $[37, 37, w^{3} - 3w + 1]$ $-4e^{2} + 12e + 16$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $-e$
59 $[59, 59, w^{2} + w - 4]$ $\phantom{-}e - 4$
61 $[61, 61, -2w^{2} + w + 8]$ $\phantom{-}2e^{2} - 5e - 10$
73 $[73, 73, -w^{3} + 5w - 1]$ $-2e^{2} + 5e + 6$
79 $[79, 79, 2w^{2} + w - 6]$ $-e^{2} + 4e + 4$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $-2e^{2} + 2e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, -w^{2} + 2]$ $-1$