# Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 5, -w^{3} + 4w]$ Label 4.4.16997.1-25.1-h Dimension 5 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 $[25, 5, -w^{3} + 4w]$ Label 4.4.16997.1-25.1-h Dimension 5 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:
$$x^{5} + 5x^{4} - 14x^{3} - 76x^{2} + 40x + 256$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $-1$
5 $[5, 5, -w^{2} + w + 2]$ $-1$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{19}{4}e^{2} - 4e + 22$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{3}{8}e^{3} - \frac{5}{2}e^{2} - \frac{7}{2}e + 14$
16 $[16, 2, 2]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{7}{2}e + 3$
19 $[19, 19, -w^{2} + w + 1]$ $-\frac{1}{8}e^{4} - \frac{3}{8}e^{3} + \frac{5}{2}e^{2} + \frac{9}{2}e - 10$
23 $[23, 23, -w^{3} + 4w + 2]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{1}{8}e^{3} - \frac{13}{4}e^{2} - \frac{1}{2}e + 20$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - \frac{9}{2}e^{2} - \frac{13}{2}e + 22$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{3}{8}e^{4} + \frac{5}{8}e^{3} - 8e^{2} - \frac{11}{2}e + 36$
29 $[29, 29, -w + 3]$ $-\frac{1}{4}e^{3} - \frac{3}{4}e^{2} + 2e + 8$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $-\frac{1}{2}e^{3} - 2e^{2} + \frac{9}{2}e + 12$
37 $[37, 37, w^{3} - 4w - 1]$ $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{11}{2}e^{2} + 2e - 22$
37 $[37, 37, w^{3} - 3w + 1]$ $-\frac{1}{4}e^{4} - \frac{3}{4}e^{3} + 4e^{2} + 6e - 12$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $\phantom{-}\frac{3}{8}e^{4} + \frac{9}{8}e^{3} - \frac{9}{2}e^{2} - \frac{15}{2}e + 6$
59 $[59, 59, w^{2} + w - 4]$ $-\frac{1}{8}e^{4} + \frac{1}{8}e^{3} + 4e^{2} - \frac{3}{2}e - 28$
61 $[61, 61, -2w^{2} + w + 8]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 8e^{2} - 12e + 30$
73 $[73, 73, -w^{3} + 5w - 1]$ $\phantom{-}\frac{1}{8}e^{4} - \frac{1}{8}e^{3} - \frac{5}{2}e^{2} + 2e$
79 $[79, 79, 2w^{2} + w - 6]$ $-\frac{3}{8}e^{4} - \frac{9}{8}e^{3} + \frac{9}{2}e^{2} + \frac{17}{2}e - 6$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{7}{8}e^{3} - e^{2} - \frac{21}{2}e + 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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