Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 23
Level $[23, 23, -w^{2} + 3]$
Label 5.5.160801.1-23.1-c
Dimension 24
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 $[23, 23, -w^{2} + 3]$
Label 5.5.160801.1-23.1-c
Dimension 24
Is CM no
Is base change no
Parent newspace dimension 39

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{24} - 2x^{23} - 54x^{22} + 101x^{21} + 1248x^{20} - 2146x^{19} - 16207x^{18} + 25069x^{17} + 130600x^{16} - 176736x^{15} - 680344x^{14} + 777066x^{13} + 2312527x^{12} - 2124130x^{11} - 5045032x^{10} + 3474263x^{9} + 6741188x^{8} - 3104376x^{7} - 5008035x^{6} + 1244497x^{5} + 1683552x^{4} - 146914x^{3} - 162972x^{2} + 5180x + 4456\)

  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 $[23, 23, -w^{2} + 3]$ $\phantom{-}1$
31 $[31, 31, w^{3} - 4w + 2]$ $...$
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
23 $[23, 23, -w^{2} + 3]$ $-1$