Properties

Label 5.5.157457.1-31.1-a
Base field 5.5.157457.1
Weight $[2, 2, 2, 2, 2]$
Level norm $31$
Level $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$
Dimension $20$
CM no
Base change no

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Base field 5.5.157457.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$
Dimension: $20$
CM: no
Base change: no
Newspace dimension: $49$

Hecke eigenvalues ($q$-expansion)

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

\(x^{20} + 5x^{19} - 25x^{18} - 149x^{17} + 220x^{16} + 1803x^{15} - 615x^{14} - 11502x^{13} - 2434x^{12} + 41796x^{11} + 22650x^{10} - 86790x^{9} - 66725x^{8} + 97197x^{7} + 92147x^{6} - 51063x^{5} - 57910x^{4} + 9731x^{3} + 14410x^{2} - 172x - 872\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}e$
5 $[5, 5, w^{2} - w - 2]$ $...$
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ $...$
13 $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ $...$
29 $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ $...$
29 $[29, 29, -w^{2} + 2w + 3]$ $...$
31 $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-1$
31 $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ $...$
32 $[32, 2, 2]$ $...$
43 $[43, 43, -w^{2} - w + 4]$ $...$
53 $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ $...$
53 $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ $...$
73 $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ $...$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $...$
81 $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ $...$
83 $[83, 83, w^{3} - w^{2} - 5w]$ $...$
89 $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ $...$
97 $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $...$
101 $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ $...$
103 $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $1$