# Properties

 Label 4.4.8069.1-13.1-b Base field 4.4.8069.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, -w^{2} + 3]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8069.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[13, 13, -w^{2} + 3]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 7x^{3} + 13x^{2} - x - 13$$
Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}e$
7 $[7, 7, w + 1]$ $-2e^{3} - 9e^{2} - 5e + 8$
7 $[7, 7, -w^{3} + 4w - 1]$ $\phantom{-}e^{2} + 4e + 1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}1$
16 $[16, 2, 2]$ $\phantom{-}e^{3} + 5e^{2} + e - 11$
17 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}e^{3} + 3e^{2} - 2e - 6$
17 $[17, 17, -w^{3} + 5w - 2]$ $\phantom{-}e + 3$
19 $[19, 19, -w^{2} - w + 4]$ $-3e^{3} - 15e^{2} - 11e + 14$
19 $[19, 19, -w^{2} - w + 1]$ $\phantom{-}e^{3} + 4e^{2} + e - 5$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $\phantom{-}3e^{3} + 13e^{2} + 4e - 22$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $-e^{3} - 4e^{2} - 5e - 4$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $-3e^{3} - 13e^{2} - 5e + 12$
43 $[43, 43, w^{3} - 6w]$ $-e^{3} - 6e^{2} - 8e + 3$
47 $[47, 47, -w^{3} - w^{2} + 5w]$ $\phantom{-}e^{3} + 8e^{2} + 10e - 13$
49 $[49, 7, w^{2} + 2w - 2]$ $\phantom{-}4e^{3} + 16e^{2} + 3e - 22$
59 $[59, 59, 2w^{3} - 8w + 3]$ $\phantom{-}2e^{3} + 9e^{2} + e - 16$
67 $[67, 67, w^{2} - w - 4]$ $\phantom{-}7e^{3} + 30e^{2} + 10e - 38$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}5e^{3} + 23e^{2} + 11e - 28$
81 $[81, 3, -3]$ $-5e^{3} - 25e^{2} - 14e + 35$
97 $[97, 97, w^{3} + w^{2} - 5w + 1]$ $-e^{3} - 3e^{2} + 5e + 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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