Properties

Label 5.5.24217.1-47.1-b
Base field 5.5.24217.1
Weight $[2, 2, 2, 2, 2]$
Level norm $47$
Level $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$
Dimension $4$
CM no
Base change no

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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: $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 3x^{3} - 10x^{2} + 28x + 4\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$47$ $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$ $-1$