# Properties

 Base field 5.5.160801.1 Weight [2, 2, 2, 2, 2] Level norm 3 Level $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ Label 5.5.160801.1-3.1-b 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 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ Label 5.5.160801.1-3.1-b Dimension 4 Is CM no Is base change no Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 3x^{3}$$ $$\mathstrut -\mathstrut 22x^{2}$$ $$\mathstrut +\mathstrut 61x$$ $$\mathstrut +\mathstrut 43$$
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 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $-e + 1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 9e - \frac{23}{2}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}e^{3} + e^{2} - 18e - 9$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 9e - \frac{1}{2}$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}\frac{1}{2}e^{3} - 9e + \frac{7}{2}$
31 $[31, 31, w^{3} - 4w + 2]$ $-e^{3} - e^{2} + 17e + 12$
32 $[32, 2, 2]$ $-\frac{1}{2}e^{3} - e^{2} + 10e + \frac{21}{2}$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}e^{3} + e^{2} - 18e - 8$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-2e^{3} - 2e^{2} + 35e + 23$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-2e + 4$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-e^{3} + 19e - 2$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $-e^{3} + 18e - 5$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-e^{3} + 18e - 1$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}4$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-2e^{3} - 3e^{2} + 35e + 39$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{1}{2}e^{3} + 9e - \frac{19}{2}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - 7e + \frac{11}{2}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-2e^{3} - 2e^{2} + 36e + 24$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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