# Properties

 Label 6.6.966125.1-59.1-b Base field 6.6.966125.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $59$ Level $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ Dimension $6$ 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: $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $26$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} + 12x^{5} + 53x^{4} + 104x^{3} + 84x^{2} + 16x - 3$$
Norm Prime Eigenvalue
5 $[5, 5, w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 3w]$ $-e - 3$
19 $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ $-e^{5} - 12e^{4} - 51e^{3} - 88e^{2} - 49e - 2$
25 $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ $-e^{5} - 10e^{4} - 33e^{3} - 40e^{2} - 15e - 4$
29 $[29, 29, -w^{4} + 4w^{2} + 1]$ $\phantom{-}2e^{3} + 11e^{2} + 13e + 2$
31 $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ $-e^{3} - 4e^{2} + e + 4$
31 $[31, 31, -w^{2} + 2]$ $\phantom{-}2e^{5} + 20e^{4} + 69e^{3} + 93e^{2} + 34e - 8$
59 $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ $\phantom{-}1$
59 $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ $-2e^{2} - 6e - 2$
59 $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ $\phantom{-}2e^{5} + 20e^{4} + 70e^{3} + 100e^{2} + 48e + 5$
61 $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ $-2e^{3} - 14e^{2} - 23e + 2$
64 $[64, 2, 2]$ $\phantom{-}2e^{5} + 21e^{4} + 75e^{3} + 103e^{2} + 43e + 6$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ $-2e^{5} - 19e^{4} - 62e^{3} - 77e^{2} - 20e + 5$
71 $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ $\phantom{-}4e^{4} + 31e^{3} + 70e^{2} + 37e - 8$
71 $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ $-3e^{5} - 27e^{4} - 78e^{3} - 72e^{2} + 2e + 6$
71 $[71, 71, w^{3} - 5w]$ $-2e^{5} - 17e^{4} - 42e^{3} - 19e^{2} + 26e + 11$
79 $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ $\phantom{-}3e^{5} + 31e^{4} + 106e^{3} + 126e^{2} + 21e - 13$
89 $[89, 89, w^{3} - w^{2} - 4w + 1]$ $-2e^{5} - 20e^{4} - 70e^{3} - 103e^{2} - 60e - 6$
101 $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ $-2e^{4} - 15e^{3} - 29e^{2} - 2e + 4$
101 $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ $\phantom{-}2e^{5} + 18e^{4} + 50e^{3} + 40e^{2} - 4e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$59$ $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ $-1$