Properties

 Label 5.5.24217.1-83.2-b Base field 5.5.24217.1 Weight $[2, 2, 2, 2, 2]$ Level norm $83$ Level $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ Dimension $3$ CM no Base change no

Related objects

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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: $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ Dimension: $3$ 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:

 $$x^{3} - 5x^{2} - 4x + 29$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{4} + w^{3} + 9w^{2} - 2w - 3]$ $\phantom{-}e$
17 $[17, 17, -2w^{4} + w^{3} + 9w^{2} - 3w - 5]$ $-e^{2} + e + 7$
17 $[17, 17, w^{2} - 2]$ $-\frac{2}{3}e^{2} + e + \frac{26}{3}$
23 $[23, 23, w^{3} - 3w]$ $\phantom{-}e^{2} - 12$
29 $[29, 29, 2w^{4} - w^{3} - 10w^{2} + 2w + 4]$ $-\frac{4}{3}e^{2} + 2e + \frac{34}{3}$
32 $[32, 2, 2]$ $\phantom{-}2e^{2} - 4e - 15$
37 $[37, 37, -w^{4} + w^{3} + 4w^{2} - 2w]$ $-\frac{4}{3}e^{2} + 4e + \frac{22}{3}$
41 $[41, 41, -3w^{4} + 2w^{3} + 14w^{2} - 5w - 7]$ $-\frac{1}{3}e^{2} - \frac{2}{3}$
43 $[43, 43, -3w^{4} + w^{3} + 14w^{2} - 3w - 6]$ $-2e^{2} + 3e + 16$
47 $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$ $-\frac{1}{3}e^{2} + \frac{16}{3}$
53 $[53, 53, 2w^{4} - w^{3} - 8w^{2} + 2w + 1]$ $\phantom{-}\frac{4}{3}e^{2} - 2e - \frac{28}{3}$
53 $[53, 53, -2w^{4} + w^{3} + 10w^{2} - 4w - 6]$ $\phantom{-}\frac{4}{3}e^{2} - 2e - \frac{28}{3}$
59 $[59, 59, -w^{4} + 4w^{2} + 1]$ $-e^{2} + 14$
59 $[59, 59, -3w^{4} + 2w^{3} + 14w^{2} - 6w - 8]$ $\phantom{-}\frac{4}{3}e^{2} - 2e - \frac{10}{3}$
61 $[61, 61, 4w^{4} - 2w^{3} - 18w^{2} + 5w + 7]$ $\phantom{-}\frac{1}{3}e^{2} - 3e - \frac{1}{3}$
61 $[61, 61, 3w^{4} - w^{3} - 15w^{2} + 2w + 7]$ $\phantom{-}\frac{2}{3}e^{2} - \frac{50}{3}$
73 $[73, 73, -4w^{4} + 2w^{3} + 18w^{2} - 7w - 6]$ $-8$
83 $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ $-\frac{5}{3}e^{2} + 2e + \frac{68}{3}$
83 $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ $\phantom{-}1$
97 $[97, 97, -2w^{4} + w^{3} + 8w^{2} - 3w + 1]$ $-\frac{2}{3}e^{2} + \frac{38}{3}$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$83$ $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ $-1$