Properties

Label 4.4.17609.1-17.2-b
Base field 4.4.17609.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{2} - w + 3]$
Dimension $20$
CM no
Base change no

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Base field 4.4.17609.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, -w^{2} - w + 3]$
Dimension: $20$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

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

\(x^{20} + 7x^{19} - 6x^{18} - 138x^{17} - 133x^{16} + 1070x^{15} + 1820x^{14} - 4096x^{13} - 9348x^{12} + 7866x^{11} + 24258x^{10} - 6530x^{9} - 33216x^{8} + 1128x^{7} + 23505x^{6} - 284x^{5} - 8657x^{4} + 821x^{3} + 1359x^{2} - 278x - 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $...$
7 $[7, 7, -w^{3} + 6w - 2]$ $...$
8 $[8, 2, w^{3} - 7w + 3]$ $...$
11 $[11, 11, -w^{3} + 6w - 4]$ $...$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $...$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}1$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $...$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $...$
41 $[41, 41, w^{2} + 2w - 4]$ $...$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $...$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $...$
59 $[59, 59, -2w^{3} + 13w - 6]$ $...$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $...$
59 $[59, 59, w^{2} + w - 1]$ $...$
59 $[59, 59, w^{2} + 2w - 6]$ $...$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $...$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $...$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $...$
81 $[81, 3, -3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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