# Properties

 Base field 4.4.2624.1 Weight [2, 2, 2, 2] Level norm 73 Level $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ Label 4.4.2624.1-73.1-d 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 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ Label 4.4.2624.1-73.1-d Dimension 5 Is CM no Is base change no Parent newspace dimension 10

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5}$$ $$\mathstrut +\mathstrut 4x^{4}$$ $$\mathstrut -\mathstrut 9x^{3}$$ $$\mathstrut -\mathstrut 49x^{2}$$ $$\mathstrut -\mathstrut 40x$$ $$\mathstrut -\mathstrut 4$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $-\frac{1}{2}e^{4} - e^{3} + \frac{11}{2}e^{2} + \frac{25}{2}e + 5$
7 $[7, 7, -w^{2} + w + 2]$ $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{13}{4}e^{2} - \frac{17}{4}e - \frac{9}{2}$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $\phantom{-}e^{4} + 2e^{3} - 11e^{2} - 26e - 8$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{13}{2}e^{2} - \frac{3}{2}e + 5$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $-\frac{3}{4}e^{4} - \frac{3}{2}e^{3} + \frac{35}{4}e^{2} + \frac{77}{4}e + \frac{13}{2}$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $-e^{3} - e^{2} + 11e + 10$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-e^{4} - e^{3} + 11e^{2} + 13e + 8$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $\phantom{-}e^{3} + e^{2} - 11e - 10$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{13}{2}e^{2} - \frac{5}{2}e + 3$
49 $[49, 7, w^{2} - 4w - 1]$ $\phantom{-}\frac{5}{4}e^{4} + \frac{3}{2}e^{3} - \frac{57}{4}e^{2} - \frac{83}{4}e - \frac{11}{2}$
71 $[71, 71, 2w - 3]$ $\phantom{-}e^{4} + 3e^{3} - 11e^{2} - 39e - 14$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}e^{4} + 4e^{3} - 11e^{2} - 48e - 20$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $-1$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $-\frac{3}{2}e^{4} - 3e^{3} + \frac{37}{2}e^{2} + \frac{79}{2}e + 5$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $-e^{4} - e^{3} + 10e^{2} + 15e + 18$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-\frac{1}{2}e^{4} - 2e^{3} + \frac{9}{2}e^{2} + \frac{49}{2}e + 13$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $\phantom{-}\frac{1}{2}e^{4} + 2e^{3} - \frac{11}{2}e^{2} - \frac{53}{2}e - 9$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $-e^{2} - 2e + 4$
81 $[81, 3, -3]$ $\phantom{-}\frac{3}{2}e^{4} + 2e^{3} - \frac{37}{2}e^{2} - \frac{47}{2}e + 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $1$