# Properties

 Label 6.6.703493.1-13.2-c Base field 6.6.703493.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $13$ Level $[13,13,-w^{5} + w^{4} + 5w^{3} - 5w^{2} - 3w + 3]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.703493.1

Generator $$w$$, with minimal polynomial $$x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[13,13,-w^{5} + w^{4} + 5w^{3} - 5w^{2} - 3w + 3]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 3x - 8$$
Norm Prime Eigenvalue
13 $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ $\phantom{-}e$
13 $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ $-1$
13 $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ $-e + 1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}2e - 3$
41 $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ $-7$
41 $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ $-e + 2$
41 $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $\phantom{-}10$
41 $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ $\phantom{-}2e - 8$
43 $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ $\phantom{-}e + 4$
43 $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ $\phantom{-}e + 4$
49 $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ $-e + 4$
64 $[64, 2, -2]$ $\phantom{-}2e - 7$
71 $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ $-e + 6$
71 $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ $\phantom{-}e + 11$
83 $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ $\phantom{-}2e + 2$
83 $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ $-3$
97 $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ $-4e + 2$
97 $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ $-4e + 2$
113 $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ $-e - 13$
113 $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ $-2e + 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,-w^{5} + w^{4} + 5w^{3} - 5w^{2} - 3w + 3]$ $1$