Properties

Label 3.3.837.1-5.1-a
Base field 3.3.837.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, -w + 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.837.1

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

Form

Weight: $[2, 2, 2]$
Level: $[5, 5, -w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2} - 2w - 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-e$
4 $[4, 2, w^{2} + w - 3]$ $\phantom{-}e - 1$
5 $[5, 5, -w + 2]$ $-1$
13 $[13, 13, -2w - 5]$ $\phantom{-}2e - 1$
25 $[25, 5, -w^{2} - 2w + 2]$ $\phantom{-}e + 2$
31 $[31, 31, -w^{2} + 2]$ $-1$
31 $[31, 31, -2w + 1]$ $-e - 4$
37 $[37, 37, 2w + 3]$ $-6e - 4$
41 $[41, 41, -w - 4]$ $\phantom{-}3e - 3$
43 $[43, 43, 2w^{2} - 2w - 7]$ $-3e - 7$
47 $[47, 47, -2w^{2} - w + 8]$ $-e - 3$
53 $[53, 53, 3w^{2} - 6w - 2]$ $\phantom{-}3$
53 $[53, 53, -2w^{2} + 3w + 18]$ $-e + 9$
53 $[53, 53, 2w - 3]$ $-6e - 3$
59 $[59, 59, 2w^{2} - 3w - 4]$ $\phantom{-}2e + 3$
61 $[61, 61, w^{2} - 2w - 4]$ $\phantom{-}4e - 4$
71 $[71, 71, 4w + 9]$ $-3e$
73 $[73, 73, 2w^{2} - 9]$ $\phantom{-}2e - 10$
79 $[79, 79, w^{2} - 4w + 2]$ $-16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 2]$ $1$