# 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-f Dimension 9 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-f Dimension 9 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:
$$x^{9}$$ $$\mathstrut -\mathstrut 3x^{8}$$ $$\mathstrut -\mathstrut 71x^{7}$$ $$\mathstrut +\mathstrut 194x^{6}$$ $$\mathstrut +\mathstrut 1730x^{5}$$ $$\mathstrut -\mathstrut 4389x^{4}$$ $$\mathstrut -\mathstrut 16430x^{3}$$ $$\mathstrut +\mathstrut 39516x^{2}$$ $$\mathstrut +\mathstrut 44872x$$ $$\mathstrut -\mathstrut 103808$$
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-1$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $...$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $...$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $...$
23 $[23, 23, -w^{2} + 3]$ $...$
31 $[31, 31, w^{3} - 4w + 2]$ $...$
32 $[32, 2, 2]$ $...$
37 $[37, 37, w^{3} - 3w - 1]$ $...$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $...$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $...$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $...$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $...$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $...$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $...$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $...$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $...$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $...$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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