Properties

Label 4.4.19796.1-13.1-a
Base field 4.4.19796.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, w^{3} - 2w^{2} - 3w + 5]$
Dimension $23$
CM no
Base change no

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Base field 4.4.19796.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, w^{3} - 2w^{2} - 3w + 5]$
Dimension: $23$
CM: no
Base change: no
Newspace dimension: $46$

Hecke eigenvalues ($q$-expansion)

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

\(x^{23} + x^{22} - 33x^{21} - 31x^{20} + 466x^{19} + 411x^{18} - 3687x^{17} - 3057x^{16} + 17971x^{15} + 14042x^{14} - 55880x^{13} - 41217x^{12} + 110998x^{11} + 76994x^{10} - 137190x^{9} - 87680x^{8} + 99858x^{7} + 54906x^{6} - 39760x^{5} - 15060x^{4} + 8571x^{3} + 1159x^{2} - 780x + 71\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}e$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $...$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $...$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $-1$
17 $[17, 17, -w^{2} - w + 3]$ $...$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $...$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $...$
31 $[31, 31, -w^{2} + w + 1]$ $...$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $...$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $...$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $...$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $...$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $...$
61 $[61, 61, 2w^{2} - 7]$ $...$
71 $[71, 71, w^{2} - 3w - 5]$ $...$
73 $[73, 73, 2w - 3]$ $...$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $...$
79 $[79, 79, 2w^{2} - 5]$ $...$
81 $[81, 3, -3]$ $...$
101 $[101, 101, 2w^{2} - 4w - 9]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $1$