Properties

Label 5.5.38569.1-17.1-a
Base field 5.5.38569.1
Weight $[2, 2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, w^{3} - 3w - 1]$
Dimension $1$
CM no
Base change no

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Base field 5.5.38569.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[17, 17, w^{3} - 3w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}5$
11 $[11, 11, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 3w]$ $\phantom{-}4$
13 $[13, 13, w^{4} - 5w^{2} + 2]$ $-4$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}1$
32 $[32, 2, 2]$ $-11$
37 $[37, 37, w^{4} + w^{3} - 5w^{2} - 5w + 4]$ $\phantom{-}3$
43 $[43, 43, w^{2} + w - 3]$ $\phantom{-}1$
43 $[43, 43, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $\phantom{-}9$
47 $[47, 47, -w^{4} - w^{3} + 6w^{2} + 4w - 5]$ $-10$
59 $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ $-9$
67 $[67, 67, -w^{3} + w^{2} + 3w - 4]$ $\phantom{-}4$
73 $[73, 73, w^{4} - 3w^{2} - w - 1]$ $-1$
73 $[73, 73, -2w^{4} - w^{3} + 9w^{2} + 5w - 6]$ $-8$
79 $[79, 79, -3w^{4} + 13w^{2} + 2w - 7]$ $-16$
79 $[79, 79, -w^{3} + 5w]$ $-10$
79 $[79, 79, -w^{4} + 3w^{2} + 1]$ $-2$
83 $[83, 83, -2w^{4} - 2w^{3} + 11w^{2} + 7w - 8]$ $\phantom{-}3$
89 $[89, 89, -w^{4} - 2w^{3} + 4w^{2} + 7w - 3]$ $-12$
101 $[101, 101, -w^{4} + 5w^{2} - w - 4]$ $\phantom{-}10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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