# Properties

 Base field 5.5.160801.1 Weight [2, 2, 2, 2, 2] Level norm 27 Level $[27, 3, -w^{3} + w^{2} + 3w - 2]$ Label 5.5.160801.1-27.2-d 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 $[27, 3, -w^{3} + w^{2} + 3w - 2]$ Label 5.5.160801.1-27.2-d Dimension 4 Is CM no Is base change no Parent newspace dimension 25

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut x^{3}$$ $$\mathstrut -\mathstrut 10x^{2}$$ $$\mathstrut -\mathstrut 19x$$ $$\mathstrut -\mathstrut 8$$
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}1$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-e^{3} + 11e + 6$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}e^{2} - 3e - 8$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}2e^{3} - e^{2} - 18e - 12$
23 $[23, 23, -w^{2} + 3]$ $-e^{3} - e^{2} + 10e + 12$
31 $[31, 31, w^{3} - 4w + 2]$ $-3e^{3} + 29e + 26$
32 $[32, 2, 2]$ $\phantom{-}4e^{3} - e^{2} - 38e - 31$
37 $[37, 37, w^{3} - 3w - 1]$ $-2e^{3} + e^{2} + 19e + 8$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $\phantom{-}2e^{3} - 21e - 22$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}4e^{3} - e^{2} - 37e - 34$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-2e^{3} + 2e^{2} + 15e + 6$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $-2e^{3} + 17e + 22$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $\phantom{-}e^{3} + 2e^{2} - 15e - 22$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $-e^{2}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-2e^{3} + e^{2} + 21e + 14$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $\phantom{-}4e^{3} - 3e^{2} - 34e - 18$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-2e^{3} + 4e^{2} + 13e - 6$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $\phantom{-}5e^{3} - 2e^{2} - 47e - 40$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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