Properties

Label 5.5.81589.1-4.1-a
Base field 5.5.81589.1
Weight $[2, 2, 2, 2, 2]$
Level norm $4$
Level $[4, 4, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$
Dimension $1$
CM no
Base change no

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Base field 5.5.81589.1

Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w^{2} - 3]$ $\phantom{-}0$
11 $[11, 11, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}2$
13 $[13, 13, -w^{3} + w^{2} + 3w - 4]$ $\phantom{-}0$
16 $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ $\phantom{-}7$
17 $[17, 17, w^{4} - 4w^{2} + 2]$ $\phantom{-}0$
31 $[31, 31, w^{4} - 4w^{2} - w + 3]$ $\phantom{-}0$
43 $[43, 43, -w^{3} + 4w - 2]$ $\phantom{-}0$
53 $[53, 53, w^{4} - 3w^{2} - 1]$ $-14$
53 $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $\phantom{-}4$
53 $[53, 53, -w^{3} - w^{2} + 3w + 4]$ $-2$
61 $[61, 61, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}14$
61 $[61, 61, w^{4} - 4w^{2} + w + 1]$ $\phantom{-}0$
61 $[61, 61, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}8$
67 $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ $-2$
71 $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ $\phantom{-}8$
71 $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ $-14$
73 $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ $-14$
73 $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ $-14$
79 $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ $\phantom{-}0$
83 $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ $\phantom{-}12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

The Atkin-Lehner eigenvalues for this form are not in the database.