Properties

Label 5.5.176281.1-13.1-c
Base field 5.5.176281.1
Weight $[2, 2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$
Dimension $12$
CM no
Base change no

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Base field 5.5.176281.1

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 3x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 13x^{11} + 49x^{10} + 29x^{9} - 524x^{8} + 554x^{7} + 1774x^{6} - 2882x^{5} - 2239x^{4} + 4436x^{3} + 636x^{2} - 1520x + 144\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{2} - w - 2]$ $...$
7 $[7, 7, -w^{2} + 2]$ $...$
11 $[11, 11, -w^{2} + 3]$ $...$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $\phantom{-}1$
23 $[23, 23, -w^{4} + 5w^{2} + w - 4]$ $...$
31 $[31, 31, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ $...$
32 $[32, 2, 2]$ $...$
37 $[37, 37, w^{3} - 3w - 1]$ $...$
41 $[41, 41, w^{4} - w^{3} - 3w^{2} + w + 1]$ $...$
47 $[47, 47, -w^{3} + w^{2} + 4w]$ $...$
61 $[61, 61, -w^{4} + 6w^{2} + w - 4]$ $...$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 4w - 3]$ $...$
71 $[71, 71, w^{4} - 6w^{2} + 7]$ $...$
73 $[73, 73, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $...$
83 $[83, 83, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ $...$
83 $[83, 83, -w^{4} + 5w^{2} + 2w - 4]$ $...$
83 $[83, 83, w^{4} - 5w^{2} + 2]$ $...$
89 $[89, 89, -2w^{4} + 2w^{3} + 9w^{2} - 6w - 4]$ $...$
101 $[101, 101, -2w^{4} + 2w^{3} + 8w^{2} - 3w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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