# Properties

 Label 6.6.371293.1-13.1-a Base field $$\Q(\zeta_{13})^+$$ Weight $[2, 2, 2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, w^{5} - 5w^{3} + 4w]$ Dimension $2$ CM no Base change yes

# Related objects

• L-function not available

## Base field $$\Q(\zeta_{13})^+$$

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

## Form

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

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 7x - 35$$
Norm Prime Eigenvalue
13 $[13, 13, w^{5} - 5w^{3} + 4w]$ $-1$
25 $[25, 5, w^{5} - 5w^{3} + 6w - 1]$ $-2$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $-2$
25 $[25, 5, w^{5} - 4w^{3} - w^{2} + 3w + 2]$ $-2$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $\phantom{-}e$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 3]$ $-e + 7$
53 $[53, 53, -w^{4} + w^{3} + 3w^{2} - 2w + 1]$ $-e + 5$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $\phantom{-}e - 2$
53 $[53, 53, -w^{5} + w^{4} + 4w^{3} - 4w^{2} - 3w + 1]$ $-e + 5$
53 $[53, 53, w^{3} - 2w - 2]$ $\phantom{-}e - 2$
53 $[53, 53, w^{5} - 5w^{3} - w^{2} + 5w]$ $-e + 5$
53 $[53, 53, -w^{4} + 4w^{2} + w - 4]$ $\phantom{-}e - 2$
64 $[64, 2, -2]$ $\phantom{-}16$
79 $[79, 79, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 9w + 2]$ $\phantom{-}e - 4$
79 $[79, 79, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 6w - 1]$ $-e + 3$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-e + 3$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 9w + 3]$ $-e + 3$
79 $[79, 79, -2w^{4} + w^{3} + 7w^{2} - 3w - 3]$ $\phantom{-}e - 4$
79 $[79, 79, -w^{5} + 6w^{3} - w^{2} - 8w + 1]$ $\phantom{-}e - 4$
103 $[103, 103, 2w^{4} - 7w^{2} - w + 3]$ $-2e + 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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