# 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-e Dimension 5 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-e Dimension 5 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:
$$x^{5} - 7x^{4} + 6x^{3} + 35x^{2} - 40x - 20$$
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 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $-1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{2}{5}e^{4} - \frac{7}{5}e^{3} - 2e^{2} + 5e + 2$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}\frac{3}{10}e^{4} - \frac{13}{10}e^{3} - 2e^{2} + \frac{15}{2}e + 4$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{6}{5}e^{3} + 7e - 1$
23 $[23, 23, -w^{2} + 3]$ $-\frac{2}{5}e^{4} + \frac{7}{5}e^{3} + 3e^{2} - 8e - 4$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}\frac{1}{10}e^{4} - \frac{1}{10}e^{3} - e^{2} - \frac{3}{2}e + 4$
32 $[32, 2, 2]$ $\phantom{-}\frac{1}{10}e^{4} - \frac{1}{10}e^{3} - e^{2} - \frac{1}{2}e$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}e^{2} - 3e - 2$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - 5e^{2} + \frac{17}{2}e + 14$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-\frac{1}{5}e^{4} + \frac{6}{5}e^{3} - 2e^{2} - 2e + 11$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-\frac{1}{5}e^{4} + \frac{1}{5}e^{3} + 2e^{2} + 2e - 2$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{3}{5}e^{4} - \frac{18}{5}e^{3} + e^{2} + 16e - 5$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-e^{3} + 4e^{2} + e - 8$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}\frac{3}{5}e^{4} - \frac{13}{5}e^{3} - e^{2} + 7e + 2$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $\phantom{-}\frac{3}{5}e^{4} - \frac{13}{5}e^{3} - e^{2} + 8e - 4$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{2}{5}e^{4} + \frac{2}{5}e^{3} + 5e^{2} - 4$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-e^{4} + 4e^{3} + 3e^{2} - 16e + 9$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-\frac{1}{5}e^{4} + \frac{6}{5}e^{3} - 2e^{2} - 2e + 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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