Properties

Label 5.5.81589.1-13.1-a
Base field 5.5.81589.1
Weight $[2, 2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{3} + w^{2} + 3w - 4]$
Dimension $4$
CM no
Base change no

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Base field 5.5.81589.1

Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[13, 13, -w^{3} + w^{2} + 3w - 4]$
Dimension: $4$
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:

\(x^{4} - 3x^{3} - x^{2} + 6x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2} - 3]$ $\phantom{-}e$
11 $[11, 11, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}2e^{3} - 3e^{2} - 6e + 3$
13 $[13, 13, -w^{3} + w^{2} + 3w - 4]$ $\phantom{-}1$
16 $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ $\phantom{-}e^{3} - 2e^{2} - 2e + 6$
17 $[17, 17, w^{4} - 4w^{2} + 2]$ $-e^{2} + e$
31 $[31, 31, w^{4} - 4w^{2} - w + 3]$ $-2e^{3} + 4e^{2} + 3e + 1$
43 $[43, 43, -w^{3} + 4w - 2]$ $\phantom{-}e^{3} + 2e^{2} - 8e - 1$
53 $[53, 53, w^{4} - 3w^{2} - 1]$ $-2e^{3} + 3e^{2} + 1$
53 $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $-3e^{3} - e^{2} + 15e + 3$
53 $[53, 53, -w^{3} - w^{2} + 3w + 4]$ $-e^{3} + 3e^{2} + 5e - 9$
61 $[61, 61, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}4e^{3} - 6e^{2} - 7e + 5$
61 $[61, 61, w^{4} - 4w^{2} + w + 1]$ $\phantom{-}3e^{3} - 7e^{2} - 8e + 12$
61 $[61, 61, w^{3} + w^{2} - 4w - 3]$ $-e^{3} + 8e^{2} - 4e - 11$
67 $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ $-3e^{2} - e + 10$
71 $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ $\phantom{-}e^{3} + 3e^{2} - 7e - 9$
71 $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ $\phantom{-}4e^{3} - 7e^{2} - 4e + 7$
73 $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ $-e^{3} - 3e^{2} + 9e + 5$
73 $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ $-3e^{3} + 2e^{2} + 10e + 3$
79 $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ $\phantom{-}4e^{3} - 12e^{2} - 3e + 17$
83 $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ $-3e^{3} + 5e^{2} + 2e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{3} + w^{2} + 3w - 4]$ $-1$