Properties

Label 5.5.138136.1-31.1-b
Base field 5.5.138136.1
Weight $[2, 2, 2, 2, 2]$
Level norm $31$
Level $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$
Dimension $1$
CM no
Base change no

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Base field 5.5.138136.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $47$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
7 $[7, 7, -2w^{4} + w^{3} + 12w^{2} + w - 5]$ $\phantom{-}2$
8 $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ $\phantom{-}3$
19 $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ $\phantom{-}8$
19 $[19, 19, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}8$
29 $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ $\phantom{-}0$
31 $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ $\phantom{-}1$
37 $[37, 37, -2w^{4} + 13w^{2} + 5w - 7]$ $\phantom{-}2$
53 $[53, 53, 3w^{4} - 2w^{3} - 18w^{2} + 3w + 9]$ $\phantom{-}6$
59 $[59, 59, 2w^{4} - 13w^{2} - 6w + 5]$ $\phantom{-}0$
61 $[61, 61, -3w^{4} + 2w^{3} + 18w^{2} - 2w - 11]$ $\phantom{-}2$
61 $[61, 61, w^{2} - w - 3]$ $-4$
61 $[61, 61, 6w^{4} - 2w^{3} - 38w^{2} - 6w + 23]$ $\phantom{-}2$
67 $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ $\phantom{-}2$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 1]$ $-4$
71 $[71, 71, -w^{2} + 3]$ $\phantom{-}0$
73 $[73, 73, 3w^{4} - w^{3} - 19w^{2} - 3w + 9]$ $-4$
79 $[79, 79, 3w^{4} - w^{3} - 19w^{2} - 4w + 11]$ $-16$
83 $[83, 83, -w^{4} - w^{3} + 7w^{2} + 8w - 3]$ $\phantom{-}0$
97 $[97, 97, -2w^{4} + w^{3} + 12w^{2} + 2w - 3]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ $-1$