# Properties

 Base field 4.4.2624.1 Weight [2, 2, 2, 2] Level norm 71 Level $[71,71,2w^{3} - 4w^{2} - 6w + 1]$ Label 4.4.2624.1-71.2-b Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.2624.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 3x^{2} + 2x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[71,71,2w^{3} - 4w^{2} - 6w + 1]$ Label 4.4.2624.1-71.2-b Dimension 5 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:
$$x^{5}$$ $$\mathstrut -\mathstrut 4x^{4}$$ $$\mathstrut -\mathstrut 8x^{3}$$ $$\mathstrut +\mathstrut 38x^{2}$$ $$\mathstrut -\mathstrut 9x$$ $$\mathstrut -\mathstrut 14$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $\phantom{-}2$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{3}{4}e^{3} - \frac{9}{4}e^{2} + \frac{25}{4}e + \frac{1}{2}$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{1}{4}e^{3} - \frac{31}{4}e^{2} - \frac{5}{4}e + \frac{11}{2}$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $-\frac{3}{4}e^{4} + \frac{3}{4}e^{3} + \frac{31}{4}e^{2} - \frac{21}{4}e - \frac{5}{2}$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $-e^{4} + 11e^{2} + 2e - 6$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $\phantom{-}\frac{3}{2}e^{4} - \frac{3}{2}e^{3} - \frac{31}{2}e^{2} + \frac{21}{2}e + 7$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-2e^{4} + 2e^{3} + 20e^{2} - 14e - 6$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - \frac{13}{4}e^{2} - \frac{41}{4}e + \frac{11}{2}$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{13}{2}e^{2} + \frac{11}{2}e - 7$
49 $[49, 7, w^{2} - 4w - 1]$ $-2e^{4} + 3e^{3} + 20e^{2} - 23e - 6$
71 $[71, 71, 2w - 3]$ $-\frac{9}{4}e^{4} + \frac{5}{4}e^{3} + \frac{93}{4}e^{2} - \frac{35}{4}e - \frac{3}{2}$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $-1$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $-\frac{9}{4}e^{4} + \frac{11}{4}e^{3} + \frac{85}{4}e^{2} - \frac{73}{4}e - \frac{5}{2}$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $\phantom{-}\frac{5}{4}e^{4} - \frac{1}{4}e^{3} - \frac{49}{4}e^{2} - \frac{5}{4}e + \frac{11}{2}$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $\phantom{-}\frac{11}{4}e^{4} - \frac{5}{4}e^{3} - \frac{115}{4}e^{2} + \frac{15}{4}e + \frac{31}{2}$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-\frac{7}{4}e^{4} + \frac{7}{4}e^{3} + \frac{75}{4}e^{2} - \frac{53}{4}e - \frac{29}{2}$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{13}{4}e^{2} + \frac{51}{4}e + \frac{15}{2}$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{5}{4}e^{3} - \frac{17}{4}e^{2} - \frac{47}{4}e + \frac{9}{2}$
81 $[81, 3, -3]$ $\phantom{-}2e^{4} - e^{3} - 22e^{2} + 5e + 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
71 $[71,71,2w^{3} - 4w^{2} - 6w + 1]$ $1$