Properties

Label 4.4.16448.1-17.1-a
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$
Dimension $21$
CM no
Base change no

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Base field 4.4.16448.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$
Dimension: $21$
CM: no
Base change: no
Newspace dimension: $42$

Hecke eigenvalues ($q$-expansion)

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

\(x^{21} - 5x^{20} - 20x^{19} + 130x^{18} + 123x^{17} - 1393x^{16} + 69x^{15} + 7969x^{14} - 4213x^{13} - 26351x^{12} + 21056x^{11} + 50898x^{10} - 48975x^{9} - 55157x^{8} + 58609x^{7} + 29907x^{6} - 34084x^{5} - 5364x^{4} + 7624x^{3} - 672x^{2} - 284x + 36\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $...$
5 $[5, 5, w - 1]$ $...$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $...$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $...$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $-1$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $...$
25 $[25, 5, -w^{2} + 3w + 1]$ $...$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $...$
31 $[31, 31, -w^{2} + 2w + 1]$ $...$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $...$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $...$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $...$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $...$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $...$
81 $[81, 3, -3]$ $...$
83 $[83, 83, -w - 3]$ $...$
83 $[83, 83, w^{2} - 3w - 7]$ $...$
89 $[89, 89, w^{2} - 2w - 7]$ $...$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $1$