Properties

Label 3.3.788.1-5.1-a
Base field 3.3.788.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, -w^{2} + 2w + 4]$
Dimension $3$
CM no
Base change no

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Base field 3.3.788.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x - 3\); narrow class number \(2\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 4x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $\phantom{-}e^{2} - e - 2$
5 $[5, 5, -w^{2} + 2w + 4]$ $\phantom{-}1$
9 $[9, 3, w^{2} - w - 7]$ $\phantom{-}e^{2} + 1$
11 $[11, 11, -w^{2} + 2w + 2]$ $-e^{2} + e + 4$
13 $[13, 13, w - 2]$ $-e^{2} + 2e + 3$
17 $[17, 17, w^{2} - 2w - 8]$ $-e^{2} - 1$
25 $[25, 5, -w^{2} + 2]$ $-2e^{2} - e + 5$
31 $[31, 31, 3w^{2} - 5w - 19]$ $-e^{2} - e + 2$
53 $[53, 53, 2w^{2} - 3w - 10]$ $-e^{2} - 2e - 1$
53 $[53, 53, w^{2} - 3w - 5]$ $\phantom{-}e^{2} + 3e - 6$
53 $[53, 53, 2w - 1]$ $-2e^{2} + 2$
59 $[59, 59, 2w^{2} - 4w - 11]$ $\phantom{-}e^{2} + 5e - 6$
59 $[59, 59, 2w^{2} - 6w - 5]$ $-4e^{2} + 2e + 6$
59 $[59, 59, 2w + 5]$ $\phantom{-}5e^{2} - 5e - 12$
67 $[67, 67, w^{2} - 3w - 7]$ $-e^{2} - 2e - 1$
71 $[71, 71, 2w^{2} - 2w - 13]$ $-e^{2} + 7e + 4$
73 $[73, 73, 2w^{2} - 4w - 7]$ $-3e^{2} - 3e + 12$
79 $[79, 79, -w^{2} + 10]$ $-2e^{2} + 3e + 5$
89 $[89, 89, 2w^{2} - w - 10]$ $\phantom{-}4e^{2} + e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w^{2} + 2w + 4]$ $-1$