# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 25, -w^{3} + 5w + 3]$ Label 4.4.16997.1-25.3-e Dimension 2 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 $[25, 25, -w^{3} + 5w + 3]$ Label 4.4.16997.1-25.3-e Dimension 2 Is CM no Is base change no Parent newspace dimension 39

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} + 2x - 10$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}3$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $-e - 3$
13 $[13, 13, w^{2} - w - 4]$ $-e + 1$
16 $[16, 2, 2]$ $\phantom{-}e - 3$
19 $[19, 19, -w^{2} + w + 1]$ $-e + 4$
23 $[23, 23, -w^{3} + 4w + 2]$ $\phantom{-}6$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $-2e - 3$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}6$
29 $[29, 29, -w + 3]$ $\phantom{-}3e + 3$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}e + 6$
37 $[37, 37, w^{3} - 4w - 1]$ $-e + 1$
37 $[37, 37, w^{3} - 3w + 1]$ $\phantom{-}e + 5$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $\phantom{-}3$
59 $[59, 59, w^{2} + w - 4]$ $\phantom{-}3e + 6$
61 $[61, 61, -2w^{2} + w + 8]$ $\phantom{-}2e + 4$
73 $[73, 73, -w^{3} + 5w - 1]$ $-e - 11$
79 $[79, 79, 2w^{2} + w - 6]$ $-4e - 6$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}e + 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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