Properties

Label 5.5.161121.1-27.1-i
Base field 5.5.161121.1
Weight $[2, 2, 2, 2, 2]$
Level norm $27$
Level $[27, 3, -w^{4} + 2w^{3} + 6w^{2} - 8w - 5]$
Dimension $1$
CM no
Base change no

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Base field 5.5.161121.1

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[27, 3, -w^{4} + 2w^{3} + 6w^{2} - 8w - 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $21$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 6w^{2} + 3w + 4]$ $-1$
3 $[3, 3, w - 1]$ $\phantom{-}0$
9 $[9, 3, -2w^{4} + 3w^{3} + 11w^{2} - 12w - 5]$ $\phantom{-}4$
17 $[17, 17, 2w^{4} - 2w^{3} - 11w^{2} + 7w + 6]$ $\phantom{-}8$
31 $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 7w - 4]$ $\phantom{-}6$
31 $[31, 31, -2w^{4} + 3w^{3} + 11w^{2} - 12w - 7]$ $-6$
32 $[32, 2, 2]$ $\phantom{-}7$
37 $[37, 37, w^{4} - 2w^{3} - 4w^{2} + 7w]$ $\phantom{-}8$
41 $[41, 41, 2w^{4} - 3w^{3} - 11w^{2} + 10w + 6]$ $\phantom{-}10$
43 $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ $-12$
43 $[43, 43, 3w^{4} - 4w^{3} - 16w^{2} + 15w + 7]$ $-6$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}4$
67 $[67, 67, -2w^{4} + 3w^{3} + 10w^{2} - 11w - 5]$ $-6$
71 $[71, 71, 4w^{4} - 5w^{3} - 22w^{2} + 18w + 12]$ $-8$
79 $[79, 79, -2w^{4} + 3w^{3} + 12w^{2} - 12w - 9]$ $\phantom{-}12$
79 $[79, 79, 3w^{4} - 3w^{3} - 16w^{2} + 8w + 4]$ $\phantom{-}0$
83 $[83, 83, w^{4} - 2w^{3} - 6w^{2} + 8w + 7]$ $\phantom{-}0$
97 $[97, 97, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 4]$ $\phantom{-}10$
107 $[107, 107, 2w^{4} - 3w^{3} - 11w^{2} + 10w + 9]$ $\phantom{-}6$
107 $[107, 107, w^{4} - w^{3} - 5w^{2} + 4w]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w^{4} - w^{3} - 6w^{2} + 3w + 4]$ $1$
$3$ $[3, 3, w - 1]$ $-1$