# Properties

 Label 4.4.13824.1-13.1-a Base field 4.4.13824.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, w^{3} - 4w + 1]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13824.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[13, 13, w^{3} - 4w + 1]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $20$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 7x^{4} + 13x^{2} - 5$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 3]$ $-e^{3} + 3e$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}e^{5} - 5e^{3} + 4e$
11 $[11, 11, -w^{2} - w + 1]$ $-e^{5} + 6e^{3} - 8e$
13 $[13, 13, w^{3} - 4w + 1]$ $\phantom{-}1$
13 $[13, 13, -w^{3} + 4w + 1]$ $-e^{4} + 3e^{2} - 1$
25 $[25, 5, -w^{2} - 2w + 1]$ $\phantom{-}e^{4} - 8e^{2} + 9$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}4e^{2} - 11$
37 $[37, 37, w^{3} - 3w - 1]$ $-2e^{4} + 9e^{2} - 7$
37 $[37, 37, w^{3} - 3w + 1]$ $-2e^{4} + 9e^{2} - 7$
59 $[59, 59, w^{2} - w - 5]$ $-2e^{5} + 8e^{3} - 2e$
59 $[59, 59, -w^{2} - w + 5]$ $\phantom{-}3e^{5} - 12e^{3} + 4e$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $\phantom{-}e^{4} - 2e^{2} + 3$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $\phantom{-}6e^{4} - 28e^{2} + 18$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}5e^{4} - 23e^{2} + 16$
73 $[73, 73, 2w - 1]$ $\phantom{-}3e^{4} - 15e^{2} + 9$
73 $[73, 73, -2w - 1]$ $-6e^{4} + 27e^{2} - 21$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}2e^{4} - 8e^{2} - 4$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $-4e^{5} + 26e^{3} - 34e$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $\phantom{-}2e^{5} - 9e^{3} + 5e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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