# Properties

 Label 6.6.966125.1-25.2-f Base field 6.6.966125.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.966125.1

Generator $$w$$, with minimal polynomial $$x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} + 4x^{3} - 9x - 5$$
Norm Prime Eigenvalue
5 $[5, 5, w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 3w]$ $\phantom{-}2e^{3} + 5e^{2} - 7e - 10$
19 $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ $-e^{3} - 4e^{2} + e + 5$
25 $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ $\phantom{-}1$
29 $[29, 29, -w^{4} + 4w^{2} + 1]$ $-e^{2} - 4e + 3$
31 $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ $-3e^{3} - 9e^{2} + 7e + 11$
31 $[31, 31, -w^{2} + 2]$ $-e^{3} - e^{2} + 5e$
59 $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ $-2e - 7$
59 $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ $-e^{2} + e + 11$
59 $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ $-4e^{3} - 11e^{2} + 15e + 20$
61 $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ $-e^{3} - e^{2} + 5e - 4$
64 $[64, 2, 2]$ $-2e^{3} - 5e^{2} + 11e + 9$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ $\phantom{-}4e^{3} + 11e^{2} - 11e - 20$
71 $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ $\phantom{-}e^{3} + 3e^{2} + 2e - 4$
71 $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ $\phantom{-}3e^{3} + 10e^{2} - 9e - 20$
71 $[71, 71, w^{3} - 5w]$ $-2e^{3} - 5e^{2} + 7e + 5$
79 $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ $\phantom{-}e^{3} + 6e^{2} + 5e - 11$
89 $[89, 89, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2e^{3} + 6e^{2} - 8e - 15$
101 $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ $-2e^{3} - 5e^{2} + 4e - 5$
101 $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ $-4e^{3} - 13e^{2} + 9e + 20$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ $-1$