# Properties

 Label 5.5.24217.1-59.1-b Base field 5.5.24217.1 Weight $[2, 2, 2, 2, 2]$ Level norm $59$ Level $[59, 59, -w^{4} + 4w^{2} + 1]$ Dimension $5$ CM no Base change no

# Related objects

• L-function not available

## Base field 5.5.24217.1

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

## Form

 Weight: $[2, 2, 2, 2, 2]$ Level: $[59, 59, -w^{4} + 4w^{2} + 1]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{5} - 3x^{4} - 15x^{3} + 39x^{2} + 15x - 25$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{4} + w^{3} + 9w^{2} - 2w - 3]$ $\phantom{-}e$
17 $[17, 17, -2w^{4} + w^{3} + 9w^{2} - 3w - 5]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{3}{5}e^{3} - 3e^{2} + \frac{34}{5}e + 2$
17 $[17, 17, w^{2} - 2]$ $-\frac{1}{10}e^{4} - \frac{1}{5}e^{3} + 2e^{2} + \frac{21}{10}e - 4$
23 $[23, 23, w^{3} - 3w]$ $-e + 1$
29 $[29, 29, 2w^{4} - w^{3} - 10w^{2} + 2w + 4]$ $-\frac{1}{5}e^{4} + \frac{3}{5}e^{3} + 3e^{2} - \frac{44}{5}e$
32 $[32, 2, 2]$ $\phantom{-}\frac{3}{10}e^{4} - \frac{9}{10}e^{3} - 4e^{2} + \frac{107}{10}e + \frac{5}{2}$
37 $[37, 37, -w^{4} + w^{3} + 4w^{2} - 2w]$ $-\frac{1}{5}e^{4} + \frac{3}{5}e^{3} + 3e^{2} - \frac{34}{5}e - 4$
41 $[41, 41, -3w^{4} + 2w^{3} + 14w^{2} - 5w - 7]$ $-\frac{1}{5}e^{4} + \frac{3}{5}e^{3} + 3e^{2} - \frac{34}{5}e$
43 $[43, 43, -3w^{4} + w^{3} + 14w^{2} - 3w - 6]$ $\phantom{-}\frac{2}{5}e^{4} - \frac{7}{10}e^{3} - 6e^{2} + \frac{43}{5}e + \frac{13}{2}$
47 $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$ $-\frac{1}{5}e^{4} + \frac{3}{5}e^{3} + 2e^{2} - \frac{29}{5}e + 7$
53 $[53, 53, 2w^{4} - w^{3} - 8w^{2} + 2w + 1]$ $-e^{2} - e + 9$
53 $[53, 53, -2w^{4} + w^{3} + 10w^{2} - 4w - 6]$ $\phantom{-}\frac{3}{10}e^{4} - \frac{2}{5}e^{3} - 4e^{2} + \frac{37}{10}e + 1$
59 $[59, 59, -w^{4} + 4w^{2} + 1]$ $\phantom{-}1$
59 $[59, 59, -3w^{4} + 2w^{3} + 14w^{2} - 6w - 8]$ $\phantom{-}2$
61 $[61, 61, 4w^{4} - 2w^{3} - 18w^{2} + 5w + 7]$ $\phantom{-}e^{2} + e - 9$
61 $[61, 61, 3w^{4} - w^{3} - 15w^{2} + 2w + 7]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{1}{10}e^{3} - 3e^{2} - \frac{11}{5}e + \frac{13}{2}$
73 $[73, 73, -4w^{4} + 2w^{3} + 18w^{2} - 7w - 6]$ $-\frac{2}{5}e^{4} + \frac{1}{5}e^{3} + 7e^{2} - \frac{13}{5}e - 12$
83 $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ $\phantom{-}\frac{1}{10}e^{4} + \frac{1}{5}e^{3} - 3e^{2} - \frac{51}{10}e + 15$
83 $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ $-\frac{2}{5}e^{4} + \frac{7}{10}e^{3} + 6e^{2} - \frac{33}{5}e - \frac{13}{2}$
97 $[97, 97, -2w^{4} + w^{3} + 8w^{2} - 3w + 1]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{3}{5}e^{3} - 3e^{2} + \frac{54}{5}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$59$ $[59, 59, -w^{4} + 4w^{2} + 1]$ $-1$