Properties

Label 3.3.568.1-5.1-a
Base field 3.3.568.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, w^{2} - w - 7]$
Dimension $3$
CM no
Base change no

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Base field 3.3.568.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[5, 5, w^{2} - w - 7]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + x^{2} - 5x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}$
5 $[5, 5, w^{2} - w - 7]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}e^{2} + e$
17 $[17, 17, -w^{2} + w + 3]$ $-e + 1$
25 $[25, 5, -w^{2} - w - 1]$ $\phantom{-}2e$
27 $[27, 3, 3]$ $-2e^{2} - e + 9$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}e^{2} + 2e - 5$
37 $[37, 37, 3w^{2} - 5w - 13]$ $-2e^{2} - 3e + 5$
41 $[41, 41, 2w - 1]$ $-e^{2} - 4e + 3$
53 $[53, 53, 5w^{2} - 9w - 21]$ $\phantom{-}2e^{2} + 2e - 10$
53 $[53, 53, 3w^{2} - 5w - 15]$ $\phantom{-}3e^{2} + 5e - 8$
53 $[53, 53, w^{2} - 3w - 7]$ $-3e^{2} - 2e + 7$
59 $[59, 59, w^{2} - 3w - 5]$ $-2e + 6$
61 $[61, 61, 2w^{2} - 4w - 9]$ $-e^{2} + 2e + 5$
61 $[61, 61, 2w - 7]$ $\phantom{-}2e - 4$
61 $[61, 61, 2w - 5]$ $-5e - 3$
67 $[67, 67, -w^{2} + w - 1]$ $-e^{2} + e + 14$
71 $[71, 71, -2w - 5]$ $\phantom{-}e^{2} + 4e - 9$
71 $[71, 71, 3w^{2} - 3w - 19]$ $-3e^{2} - 2e + 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w^{2} - w - 7]$ $-1$