# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 5, -w^{3} + 4w]$ Label 4.4.16997.1-25.1-d Dimension 1 CM no Base change no

# Related objects

## 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 $[25, 5, -w^{3} + 4w]$ Label 4.4.16997.1-25.1-d Dimension 1 Is CM no Is base change no Parent newspace dimension 39

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, w]$ $-1$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}1$
7 $[7, 7, -w^{2} + 2]$ $-3$
13 $[13, 13, -w^{2} + 3]$ $-6$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}3$
16 $[16, 2, 2]$ $\phantom{-}5$
19 $[19, 19, -w^{2} + w + 1]$ $-6$
23 $[23, 23, -w^{3} + 4w + 2]$ $-6$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}3$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $-1$
29 $[29, 29, -w + 3]$ $-10$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}2$
37 $[37, 37, w^{3} - 4w - 1]$ $\phantom{-}8$
37 $[37, 37, w^{3} - 3w + 1]$ $-8$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $-3$
59 $[59, 59, w^{2} + w - 4]$ $\phantom{-}6$
61 $[61, 61, -2w^{2} + w + 8]$ $\phantom{-}14$
73 $[73, 73, -w^{3} + 5w - 1]$ $-2$
79 $[79, 79, 2w^{2} + w - 6]$ $\phantom{-}6$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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