# Properties

 Base field 4.4.8069.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 25, -w^{3} - w^{2} + 3w + 2]$ Label 4.4.8069.1-25.1-e Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8069.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 5x^{2} + 5x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[25, 25, -w^{3} - w^{2} + 3w + 2]$ Label 4.4.8069.1-25.1-e Dimension 4 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 19x^{2}$$ $$\mathstrut +\mathstrut 75$$
Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}0$
7 $[7, 7, w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 4w - 1]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $-\frac{1}{5}e^{3} + \frac{9}{5}e$
16 $[16, 2, 2]$ $-e^{2} + 11$
17 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{14}{5}e$
17 $[17, 17, -w^{3} + 5w - 2]$ $\phantom{-}e^{2} - 6$
19 $[19, 19, -w^{2} - w + 4]$ $-e^{2} + 14$
19 $[19, 19, -w^{2} - w + 1]$ $-\frac{3}{5}e^{3} + \frac{32}{5}e$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $-\frac{2}{5}e^{3} + \frac{13}{5}e$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{24}{5}e$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{23}{5}e$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}2e^{2} - 14$
47 $[47, 47, -w^{3} - w^{2} + 5w]$ $\phantom{-}2e^{2} - 15$
49 $[49, 7, w^{2} + 2w - 2]$ $-5$
59 $[59, 59, 2w^{3} - 8w + 3]$ $\phantom{-}\frac{3}{5}e^{3} - \frac{32}{5}e$
67 $[67, 67, w^{2} - w - 4]$ $-\frac{2}{5}e^{3} + \frac{18}{5}e$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}0$
81 $[81, 3, -3]$ $\phantom{-}3e^{2} - 25$
97 $[97, 97, w^{3} + w^{2} - 5w + 1]$ $-3e^{2} + 25$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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