# Properties

 Label 6.6.1279733.1-29.3-f Base field 6.6.1279733.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $29$ Level $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

# Learn more

## Base field 6.6.1279733.1

Generator $$w$$, with minimal polynomial $$x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $22$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 3x - 2$$
Norm Prime Eigenvalue
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ $\phantom{-}e - 4$
7 $[7, 7, -w^{4} + w^{3} + 4w^{2} - w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 3w - 3]$ $-e + 4$
29 $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ $-4e + 8$
29 $[29, 29, w^{4} - 5w^{2} - 2w + 4]$ $\phantom{-}e - 6$
29 $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ $\phantom{-}1$
29 $[29, 29, -w^{2} + w + 1]$ $-3e + 4$
41 $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ $-2e + 2$
43 $[43, 43, 2w^{3} - 2w^{2} - 7w + 3]$ $-e - 8$
43 $[43, 43, w^{3} - w^{2} - 2w + 1]$ $-2$
64 $[64, 2, -2]$ $-2e - 3$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $\phantom{-}4e - 4$
71 $[71, 71, w^{5} - 2w^{4} - 2w^{3} + 5w^{2} - 3w - 1]$ $\phantom{-}12$
83 $[83, 83, -2w^{4} + 3w^{3} + 6w^{2} - 7w + 2]$ $\phantom{-}14$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ $\phantom{-}4e - 14$
83 $[83, 83, -w^{5} + 3w^{4} + w^{3} - 9w^{2} + 5w + 3]$ $-3e + 2$
83 $[83, 83, w^{5} - 7w^{3} + 10w - 1]$ $\phantom{-}2e - 12$
97 $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 1]$ $-4e + 8$
97 $[97, 97, w^{5} - 5w^{3} - w^{2} + 3w - 3]$ $-2e - 4$
113 $[113, 113, w^{4} - w^{3} - 4w^{2} + w + 4]$ $\phantom{-}8e - 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ $-1$