# Properties

 Base field 5.5.160801.1 Weight [2, 2, 2, 2, 2] Level norm 9 Level $[9, 3, -w^{4} + 5w^{2} - 3]$ Label 5.5.160801.1-9.1-e Dimension 4 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 $[9, 3, -w^{4} + 5w^{2} - 3]$ Label 5.5.160801.1-9.1-e Dimension 4 Is CM no Is base change no Parent newspace dimension 13

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 10x^{3} + 30x^{2} - 25x + 5$$
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-e^{2} + 5e - 3$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}1$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}e$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-2e^{3} + 16e^{2} - 34e + 13$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}e^{3} - 8e^{2} + 19e - 11$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}e^{3} - 10e^{2} + 28e - 13$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}2e^{2} - 8e - 1$
31 $[31, 31, w^{3} - 4w + 2]$ $-e^{3} + 7e^{2} - 10e - 5$
32 $[32, 2, 2]$ $-2e^{3} + 13e^{2} - 18e + 1$
37 $[37, 37, w^{3} - 3w - 1]$ $-2e^{3} + 15e^{2} - 29e + 11$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $\phantom{-}2e^{3} - 13e^{2} + 20e - 10$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}3e^{3} - 22e^{2} + 41e - 10$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $\phantom{-}3e^{3} - 22e^{2} + 39e - 7$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}3e^{3} - 21e^{2} + 33e - 3$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-e^{3} + 8e^{2} - 16e + 14$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}e^{3} - 5e^{2} + e + 7$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-e^{3} - e^{2} + 26e - 7$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-4e^{3} + 26e^{2} - 42e + 23$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $\phantom{-}2e^{3} - 23e^{2} + 72e - 32$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $\phantom{-}2e^{3} - 7e^{2} - 10e + 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-1$