# Properties

 Base field 4.4.8789.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 25, w^{3} - w^{2} - 6w]$ Label 4.4.8789.1-25.1-f Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} - 2x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[25, 25, w^{3} - w^{2} - 6w]$ Label 4.4.8789.1-25.1-f Dimension 4 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 8x^{3} + 9x^{2} + 44x - 73$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}0$
7 $[7, 7, w - 1]$ $\phantom{-}e$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + \frac{10}{3}e - \frac{28}{3}$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-\frac{1}{3}e^{3} + \frac{7}{3}e^{2} + \frac{1}{3}e - \frac{37}{3}$
16 $[16, 2, 2]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{11}{3}e^{2} - \frac{5}{3}e + \frac{56}{3}$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + \frac{7}{3}e - \frac{16}{3}$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{10}{3}e + \frac{28}{3}$
17 $[17, 17, -w^{2} + 2w + 1]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + \frac{7}{3}e - \frac{16}{3}$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{11}{3}e^{2} - \frac{5}{3}e + \frac{50}{3}$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{11}{3}e^{2} - \frac{11}{3}e + \frac{68}{3}$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{7}{3}e^{2} - \frac{1}{3}e + \frac{49}{3}$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + \frac{4}{3}e - \frac{10}{3}$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-\frac{1}{3}e^{3} + \frac{7}{3}e^{2} + \frac{1}{3}e - \frac{37}{3}$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{8}{3}e^{2} - \frac{11}{3}e + \frac{20}{3}$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{11}{3}e^{2} - \frac{14}{3}e + \frac{89}{3}$
61 $[61, 61, -w - 3]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + \frac{7}{3}e - \frac{19}{3}$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} + \frac{2}{3}e + \frac{10}{3}$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $-e^{3} + 4e^{2} + 7e - 21$
81 $[81, 3, -3]$ $\phantom{-}e^{2} - 3e - 8$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-\frac{4}{3}e^{3} + \frac{19}{3}e^{2} + \frac{22}{3}e - \frac{97}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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