Properties

Label 5.5.70601.1-17.1-a
Base field 5.5.70601.1
Weight $[2, 2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, w^{2} - 2]$
Dimension $1$
CM no
Base change no

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Base field 5.5.70601.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[17, 17, w^{2} - 2]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, w^{4} - 6w^{2} - 2w + 4]$ $\phantom{-}1$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - w - 4]$ $-1$
11 $[11, 11, -2w^{4} + w^{3} + 10w^{2} + w - 3]$ $-3$
11 $[11, 11, w^{4} - 6w^{2} - 3w + 3]$ $-3$
17 $[17, 17, w^{2} - 2]$ $-1$
23 $[23, 23, -w^{3} + w^{2} + 3w]$ $\phantom{-}0$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ $-4$
29 $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ $\phantom{-}3$
32 $[32, 2, -2]$ $-9$
47 $[47, 47, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-6$
47 $[47, 47, w^{3} - w^{2} - 4w - 1]$ $\phantom{-}6$
53 $[53, 53, -w^{4} + 7w^{2} - 3]$ $-6$
53 $[53, 53, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 2]$ $\phantom{-}6$
53 $[53, 53, 3w^{4} - 2w^{3} - 16w^{2} + 8]$ $-6$
67 $[67, 67, -w^{4} + 6w^{2} + 4w - 3]$ $\phantom{-}7$
73 $[73, 73, 2w^{4} - 12w^{2} - 4w + 5]$ $\phantom{-}2$
83 $[83, 83, w^{4} - 5w^{2} - 3w + 3]$ $-6$
97 $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $-2$
103 $[103, 103, 2w^{3} - 3w^{2} - 7w + 3]$ $-8$
109 $[109, 109, -3w^{4} + 2w^{3} + 14w^{2} + w - 6]$ $\phantom{-}1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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