# Properties

 Label 5.5.24217.1-83.1-d Base field 5.5.24217.1 Weight $[2, 2, 2, 2, 2]$ Level norm $83$ Level $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ 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: $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{5} + x^{4} - 20x^{3} - 12x^{2} + 48x - 16$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{4} + w^{3} + 9w^{2} - 2w - 3]$ $\phantom{-}e$
17 $[17, 17, -2w^{4} + w^{3} + 9w^{2} - 3w - 5]$ $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{19}{4}e^{2} + 7e - 9$
17 $[17, 17, w^{2} - 2]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - 5e^{2} - 4e + 8$
23 $[23, 23, w^{3} - 3w]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{19}{4}e^{2} - 7e + 10$
29 $[29, 29, 2w^{4} - w^{3} - 10w^{2} + 2w + 4]$ $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + 4e^{2} + 3e$
32 $[32, 2, 2]$ $-\frac{3}{8}e^{4} - \frac{3}{8}e^{3} + 7e^{2} + 5e - 10$
37 $[37, 37, -w^{4} + w^{3} + 4w^{2} - 2w]$ $\phantom{-}\frac{3}{8}e^{4} + \frac{7}{8}e^{3} - 7e^{2} - \frac{23}{2}e + 12$
41 $[41, 41, -3w^{4} + 2w^{3} + 14w^{2} - 5w - 7]$ $\phantom{-}\frac{3}{8}e^{4} + \frac{3}{8}e^{3} - \frac{15}{2}e^{2} - \frac{7}{2}e + 12$
43 $[43, 43, -3w^{4} + w^{3} + 14w^{2} - 3w - 6]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - 5e^{2} - \frac{23}{2}e + 12$
47 $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$ $-\frac{3}{8}e^{4} - \frac{3}{8}e^{3} + \frac{15}{2}e^{2} + \frac{9}{2}e - 10$
53 $[53, 53, 2w^{4} - w^{3} - 8w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - 4e^{2} - 3e + 2$
53 $[53, 53, -2w^{4} + w^{3} + 10w^{2} - 4w - 6]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{19}{4}e^{2} - 9e + 11$
59 $[59, 59, -w^{4} + 4w^{2} + 1]$ $-\frac{3}{4}e^{4} - \frac{5}{4}e^{3} + 14e^{2} + \frac{41}{2}e - 22$
59 $[59, 59, -3w^{4} + 2w^{3} + 14w^{2} - 6w - 8]$ $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{7}{2}e^{2} + \frac{7}{2}e + 4$
61 $[61, 61, 4w^{4} - 2w^{3} - 18w^{2} + 5w + 7]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{17}{4}e^{2} + e + 8$
61 $[61, 61, 3w^{4} - w^{3} - 15w^{2} + 2w + 7]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{17}{4}e^{2} + e + 8$
73 $[73, 73, -4w^{4} + 2w^{3} + 18w^{2} - 7w - 6]$ $-\frac{1}{4}e^{4} - \frac{3}{4}e^{3} + \frac{9}{2}e^{2} + 12e - 2$
83 $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ $\phantom{-}1$
83 $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - \frac{9}{2}e^{2} - 13e + 2$
97 $[97, 97, -2w^{4} + w^{3} + 8w^{2} - 3w + 1]$ $\phantom{-}\frac{3}{8}e^{4} + \frac{7}{8}e^{3} - 7e^{2} - \frac{31}{2}e + 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$83$ $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ $-1$