Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 31
Level $[31, 31, w^{3} - 4w + 2]$
Label 5.5.160801.1-31.1-b
Dimension 21
CM no
Base change no

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Base field 5.5.160801.1

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

Form

Weight [2, 2, 2, 2, 2]
Level $[31, 31, w^{3} - 4w + 2]$
Label 5.5.160801.1-31.1-b
Dimension 21
Is CM no
Is base change no
Parent newspace dimension 49

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} + 6x^{20} - 24x^{19} - 202x^{18} + 117x^{17} + 2707x^{16} + 1601x^{15} - 18409x^{14} - 23085x^{13} + 65974x^{12} + 121558x^{11} - 109018x^{10} - 317596x^{9} + 9969x^{8} + 399443x^{7} + 196325x^{6} - 165947x^{5} - 178344x^{4} - 44116x^{3} + 6224x^{2} + 3904x + 384\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $...$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $...$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $...$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $...$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $...$
23 $[23, 23, -w^{2} + 3]$ $...$
31 $[31, 31, w^{3} - 4w + 2]$ $-1$
32 $[32, 2, 2]$ $...$
37 $[37, 37, w^{3} - 3w - 1]$ $...$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $...$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $...$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $...$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $...$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $...$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $...$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $...$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $...$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $...$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, w^{3} - 4w + 2]$ $1$