# Properties

 Base field 5.5.65657.1 Weight [2, 2, 2, 2, 2] Level norm 45 Level $[45, 45, -w^{3} + 4w]$ Label 5.5.65657.1-45.1-c Dimension 1 CM no Base change no

# Related objects

## Base field 5.5.65657.1

Generator $$w$$, with minimal polynomial $$x^{5} - x^{4} - 5x^{3} + 2x^{2} + 5x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2, 2] Level $[45, 45, -w^{3} + 4w]$ Label 5.5.65657.1-45.1-c Dimension 1 Is CM no Is base change no Parent newspace dimension 7

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $\phantom{-}0$
5 $[5, 5, w^{2} - w - 2]$ $\phantom{-}1$
19 $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ $\phantom{-}4$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}2$
29 $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ $-2$
32 $[32, 2, 2]$ $-1$
37 $[37, 37, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}10$
41 $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ $\phantom{-}2$
43 $[43, 43, -2w^{4} + 3w^{3} + 8w^{2} - 8w - 6]$ $\phantom{-}0$
47 $[47, 47, w^{4} - 2w^{3} - 5w^{2} + 6w + 5]$ $\phantom{-}4$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ $-6$
61 $[61, 61, w^{2} - 2w - 3]$ $-6$
67 $[67, 67, w^{4} - w^{3} - 4w^{2} + 3w]$ $-4$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ $\phantom{-}8$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 5]$ $\phantom{-}0$
71 $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 5w + 3]$ $\phantom{-}6$
71 $[71, 71, 2w^{4} - 2w^{3} - 8w^{2} + 5w + 4]$ $\phantom{-}12$
73 $[73, 73, -2w^{4} + 2w^{3} + 9w^{2} - 5w - 6]$ $-14$
81 $[81, 3, -2w^{4} + 3w^{3} + 10w^{2} - 9w - 10]$ $-8$
97 $[97, 97, -2w^{4} + 3w^{3} + 7w^{2} - 5w - 4]$ $\phantom{-}6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $1$
5 $[5, 5, w^{2} - w - 2]$ $-1$