Properties

 Base field 5.5.160801.1 Weight [2, 2, 2, 2, 2] Level norm 13 Level $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ Label 5.5.160801.1-13.1-a Dimension 2 CM no Base change no

Related objects

• L-function not available

Base field 5.5.160801.1

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

Form

 Weight [2, 2, 2, 2, 2] Level $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ Label 5.5.160801.1-13.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 3x$$ $$\mathstrut +\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-2e - 4$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}3$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-1$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}e$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}e$
23 $[23, 23, -w^{2} + 3]$ $-2e - 9$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}4e + 5$
32 $[32, 2, 2]$ $\phantom{-}e + 2$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}2e + 3$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-9e - 16$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-3e + 6$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-2e - 7$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $-7$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $\phantom{-}4e + 5$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $-4e - 6$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-4e - 15$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-e + 2$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-4e - 14$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-2e - 9$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $1$