# Properties

 Base field 5.5.160801.1 Weight [2, 2, 2, 2, 2] Level norm 27 Level $[27, 27, w^{4} - w^{3} - 5w^{2} + 4w + 1]$ Label 5.5.160801.1-27.3-h 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 $[27, 27, w^{4} - w^{3} - 5w^{2} + 4w + 1]$ Label 5.5.160801.1-27.3-h Dimension 5 Is CM no Is base change no Parent newspace dimension 24

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5}$$ $$\mathstrut -\mathstrut 4x^{4}$$ $$\mathstrut -\mathstrut 13x^{3}$$ $$\mathstrut +\mathstrut 44x^{2}$$ $$\mathstrut +\mathstrut 42x$$ $$\mathstrut -\mathstrut 118$$
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}0$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $-e^{3} + 4e^{2} + 7e - 23$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-\frac{1}{8}e^{4} + \frac{7}{8}e^{3} - \frac{13}{2}e + \frac{9}{4}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $-\frac{1}{4}e^{4} + \frac{7}{4}e^{3} - e^{2} - 10e + \frac{25}{2}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{3}{4}e^{3} - 3e^{2} + 4e + \frac{7}{2}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{1}{4}e^{4} + \frac{7}{4}e^{3} - 2e^{2} - 10e + \frac{45}{2}$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{4}e^{3} + e^{2} + 9e - \frac{25}{2}$
32 $[32, 2, 2]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{1}{8}e^{3} - 4e^{2} - \frac{1}{2}e + \frac{59}{4}$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}\frac{5}{8}e^{4} - \frac{19}{8}e^{3} - 6e^{2} + \frac{29}{2}e + \frac{35}{4}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-e^{3} + 5e^{2} + 4e - 26$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}\frac{5}{8}e^{4} - \frac{27}{8}e^{3} - e^{2} + \frac{39}{2}e - \frac{69}{4}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-\frac{5}{8}e^{4} + \frac{19}{8}e^{3} + 6e^{2} - \frac{25}{2}e - \frac{67}{4}$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{3}{4}e^{3} - 3e^{2} + 4e + \frac{13}{2}$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-\frac{7}{8}e^{4} + \frac{25}{8}e^{3} + 8e^{2} - \frac{37}{2}e - \frac{33}{4}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{7}{8}e^{3} + \frac{7}{2}e - \frac{13}{4}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-2e^{3} + 9e^{2} + 14e - 48$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{1}{2}e^{4} + \frac{7}{2}e^{3} - 4e^{2} - 20e + 42$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-\frac{5}{4}e^{4} + \frac{19}{4}e^{3} + 11e^{2} - 25e - \frac{39}{2}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-\frac{1}{4}e^{4} + \frac{7}{4}e^{3} - e^{2} - 10e + \frac{25}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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