Properties

Base field 4.4.2777.1
Weight [2, 2, 2, 2]
Level norm 16
Level $[16, 2, 2]$
Label 4.4.2777.1-16.1-a
Dimension 1
CM no
Base change no

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Base field 4.4.2777.1

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

Form

Weight [2, 2, 2, 2]
Level $[16, 2, 2]$
Label 4.4.2777.1-16.1-a
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
8 $[8, 2, -w^{3} + w^{2} + 4w - 1]$ $-1$
11 $[11, 11, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}0$
23 $[23, 23, -w^{3} + 4w + 1]$ $\phantom{-}0$
23 $[23, 23, -w^{2} + 2w + 3]$ $\phantom{-}0$
31 $[31, 31, w^{3} - 2w^{2} - w + 3]$ $\phantom{-}8$
37 $[37, 37, -w^{3} + 3w + 3]$ $\phantom{-}2$
37 $[37, 37, -2w^{3} + 3w^{2} + 6w - 3]$ $\phantom{-}2$
41 $[41, 41, w^{3} - 2w^{2} - 3w + 1]$ $-6$
41 $[41, 41, -2w^{3} + 2w^{2} + 6w - 1]$ $-6$
43 $[43, 43, -w^{2} + w + 5]$ $\phantom{-}8$
47 $[47, 47, 2w^{2} - 3w - 5]$ $\phantom{-}0$
53 $[53, 53, -w^{3} + 3w^{2} + w - 7]$ $-6$
53 $[53, 53, -2w^{2} + 2w + 5]$ $\phantom{-}6$
59 $[59, 59, 2w^{2} - w - 7]$ $\phantom{-}0$
61 $[61, 61, 2w^{2} - w - 3]$ $\phantom{-}14$
61 $[61, 61, 2w^{2} - w - 5]$ $\phantom{-}2$
67 $[67, 67, 2w^{3} - 2w^{2} - 7w + 3]$ $\phantom{-}8$
67 $[67, 67, 2w^{3} - 2w^{2} - 7w - 1]$ $\phantom{-}8$
71 $[71, 71, 2w^{3} - 4w^{2} - 4w + 7]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $1$
8 $[8, 2, -w^{3} + w^{2} + 4w - 1]$ $1$