# 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-c 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-c 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:
$$x^{4}$$ $$\mathstrut +\mathstrut 5x^{3}$$ $$\mathstrut -\mathstrut 8x^{2}$$ $$\mathstrut -\mathstrut 19x$$ $$\mathstrut +\mathstrut 20$$
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 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $-1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-\frac{1}{7}e^{3} - \frac{2}{7}e^{2} + 3e - \frac{2}{7}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $-\frac{2}{7}e^{3} - \frac{11}{7}e^{2} + e - \frac{4}{7}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $-\frac{2}{7}e^{3} - \frac{11}{7}e^{2} + \frac{38}{7}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{3}{7}e^{3} - \frac{13}{7}e^{2} + 2e + \frac{8}{7}$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}\frac{3}{7}e^{3} + \frac{20}{7}e^{2} + e - \frac{78}{7}$
32 $[32, 2, 2]$ $-\frac{4}{7}e^{3} - \frac{29}{7}e^{2} - 2e + \frac{83}{7}$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}\frac{2}{7}e^{3} + \frac{11}{7}e^{2} - e - \frac{38}{7}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $\phantom{-}\frac{8}{7}e^{3} + \frac{44}{7}e^{2} - 3e - \frac{110}{7}$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}\frac{4}{7}e^{3} + \frac{29}{7}e^{2} + e - \frac{118}{7}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $\phantom{-}\frac{4}{7}e^{3} + \frac{22}{7}e^{2} - 3e - \frac{90}{7}$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{4}{7}e^{3} + \frac{22}{7}e^{2} + e - \frac{6}{7}$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $\phantom{-}\frac{5}{7}e^{3} + \frac{24}{7}e^{2} - 7e - \frac{60}{7}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $-e^{2} - 6e$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-\frac{8}{7}e^{3} - \frac{51}{7}e^{2} + e + \frac{138}{7}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $\phantom{-}e^{2} + 4e - 8$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-\frac{2}{7}e^{3} - \frac{4}{7}e^{2} + 5e + \frac{52}{7}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-\frac{3}{7}e^{3} - \frac{20}{7}e^{2} - 3e + \frac{50}{7}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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