# Properties

 Base field 4.4.8789.1 Weight [2, 2, 2, 2] Level norm 17 Level $[17, 17, -w^{2} + 2w + 1]$ Label 4.4.8789.1-17.3-d Dimension 5 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 $[17, 17, -w^{2} + 2w + 1]$ Label 4.4.8789.1-17.3-d Dimension 5 Is CM no Is base change no Parent newspace dimension 11

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5} - 4x^{4} - 14x^{3} + 72x^{2} - 56x - 24$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{1}{10}e^{4} - \frac{3}{10}e^{3} - \frac{17}{10}e^{2} + 5e - \frac{8}{5}$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{3}{5}e^{3} - \frac{17}{5}e^{2} + 10e - \frac{6}{5}$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-\frac{1}{10}e^{4} + \frac{3}{10}e^{3} + \frac{11}{5}e^{2} - 4e - \frac{32}{5}$
16 $[16, 2, 2]$ $\phantom{-}e - 1$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-\frac{7}{20}e^{4} + \frac{3}{10}e^{3} + \frac{31}{5}e^{2} - 7e - \frac{42}{5}$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}\frac{3}{20}e^{4} - \frac{1}{5}e^{3} - \frac{23}{10}e^{2} + 4e - \frac{12}{5}$
17 $[17, 17, -w^{2} + 2w + 1]$ $-1$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{9}{2}e^{2} + 10e + 2$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $\phantom{-}\frac{1}{20}e^{4} - \frac{2}{5}e^{3} - \frac{3}{5}e^{2} + 7e - \frac{24}{5}$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - 8e + 6$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1}{10}e^{4} + \frac{3}{10}e^{3} + \frac{6}{5}e^{2} - 4e + \frac{28}{5}$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-\frac{9}{20}e^{4} + \frac{3}{5}e^{3} + \frac{37}{5}e^{2} - 11e - \frac{14}{5}$
47 $[47, 47, w^{3} - 7w - 4]$ $-\frac{1}{2}e^{3} + 8e$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 8e^{2} - 12e$
61 $[61, 61, -w - 3]$ $\phantom{-}\frac{13}{20}e^{4} - \frac{7}{10}e^{3} - \frac{59}{5}e^{2} + 15e + \frac{88}{5}$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-\frac{13}{20}e^{4} + \frac{6}{5}e^{3} + \frac{54}{5}e^{2} - 23e - \frac{8}{5}$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}\frac{3}{5}e^{4} - \frac{13}{10}e^{3} - \frac{46}{5}e^{2} + 25e - \frac{38}{5}$
81 $[81, 3, -3]$ $\phantom{-}\frac{7}{20}e^{4} - \frac{13}{10}e^{3} - \frac{31}{5}e^{2} + 23e - \frac{28}{5}$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}\frac{1}{20}e^{4} - \frac{2}{5}e^{3} - \frac{3}{5}e^{2} + 7e - \frac{24}{5}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{2} + 2w + 1]$ $1$