# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 25, -w^{3} + 5w + 3]$ Label 4.4.16997.1-25.3-f Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16997.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[25, 25, -w^{3} + 5w + 3]$ Label 4.4.16997.1-25.3-f Dimension 3 Is CM no Is base change no Parent newspace dimension 39

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} - 13x - 13$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}e$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}\frac{2}{5}e^{2} + \frac{2}{5}e - \frac{24}{5}$
13 $[13, 13, -w^{2} + 3]$ $-\frac{1}{5}e^{2} + \frac{4}{5}e + \frac{32}{5}$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}\frac{3}{5}e^{2} - \frac{2}{5}e - \frac{16}{5}$
16 $[16, 2, 2]$ $\phantom{-}\frac{2}{5}e^{2} - \frac{8}{5}e - \frac{9}{5}$
19 $[19, 19, -w^{2} + w + 1]$ $\phantom{-}\frac{2}{5}e^{2} - \frac{8}{5}e - \frac{24}{5}$
23 $[23, 23, -w^{3} + 4w + 2]$ $\phantom{-}\frac{4}{5}e^{2} - \frac{6}{5}e - \frac{38}{5}$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{3}{5}e^{2} - \frac{7}{5}e - \frac{46}{5}$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{6}{5}e^{2} - \frac{14}{5}e - \frac{57}{5}$
29 $[29, 29, -w + 3]$ $\phantom{-}\frac{3}{5}e^{2} - \frac{7}{5}e - \frac{16}{5}$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $-\frac{4}{5}e^{2} + \frac{6}{5}e - \frac{2}{5}$
37 $[37, 37, w^{3} - 4w - 1]$ $-\frac{2}{5}e^{2} + \frac{3}{5}e + \frac{14}{5}$
37 $[37, 37, w^{3} - 3w + 1]$ $\phantom{-}\frac{1}{5}e^{2} - \frac{4}{5}e - \frac{22}{5}$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $\phantom{-}\frac{3}{5}e^{2} + \frac{3}{5}e + \frac{4}{5}$
59 $[59, 59, w^{2} + w - 4]$ $-2e + 2$
61 $[61, 61, -2w^{2} + w + 8]$ $\phantom{-}\frac{6}{5}e^{2} - \frac{14}{5}e - \frac{17}{5}$
73 $[73, 73, -w^{3} + 5w - 1]$ $\phantom{-}\frac{7}{5}e^{2} + \frac{7}{5}e - \frac{64}{5}$
79 $[79, 79, 2w^{2} + w - 6]$ $\phantom{-}\frac{2}{5}e^{2} - \frac{8}{5}e - \frac{24}{5}$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}2e^{2} - 4e - 18$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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