# Properties

 Label 6.6.1202933.1-35.1-d Base field 6.6.1202933.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $35$ Level $[35, 35, 2w^{5} - 11w^{3} - 4w^{2} + 7w + 1]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.1202933.1

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

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[35, 35, 2w^{5} - 11w^{3} - 4w^{2} + 7w + 1]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $17$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 10x + 22$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ $\phantom{-}1$
7 $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ $-1$
19 $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ $\phantom{-}e$
23 $[23, 23, -w^{2} + w + 2]$ $-3e - 17$
25 $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ $\phantom{-}e + 6$
41 $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ $-3e - 19$
47 $[47, 47, w^{3} - w^{2} - 4w]$ $-3e - 20$
53 $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ $\phantom{-}3e + 12$
59 $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ $\phantom{-}2e + 10$
61 $[61, 61, w^{2} - 2w - 2]$ $-3e - 10$
64 $[64, 2, -2]$ $\phantom{-}2e + 11$
67 $[67, 67, -w^{4} + 6w^{2} + w - 3]$ $-e - 5$
67 $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ $\phantom{-}e - 6$
73 $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ $-e - 14$
73 $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ $\phantom{-}7$
79 $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ $\phantom{-}9e + 47$
83 $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ $-2e - 16$
89 $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ $-2e - 11$
97 $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}6e + 38$
97 $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ $-6e - 34$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ $-1$
$7$ $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ $1$