Properties

Base field 4.4.9248.1
Weight [2, 2, 2, 2]
Level norm 16
Level $[16, 4, -w^{2} + 3]$
Label 4.4.9248.1-16.3-f
Dimension 4
CM no
Base change yes

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Base field 4.4.9248.1

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

Form

Weight [2, 2, 2, 2]
Level $[16, 4, -w^{2} + 3]$
Label 4.4.9248.1-16.3-f
Dimension 4
Is CM no
Is base change yes
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 9x^{2} + 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}2e$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}2e$
19 $[19, 19, -w^{3} + 3w + 1]$ $-e^{3} + 5e$
19 $[19, 19, -w^{3} + 3w - 1]$ $-e^{3} + 5e$
43 $[43, 43, -w^{2} + w - 1]$ $\phantom{-}2e^{2} - 14$
43 $[43, 43, w^{2} + w + 1]$ $\phantom{-}2e^{2} - 14$
49 $[49, 7, w^{3} + w^{2} - 6w - 3]$ $-2e^{3} + 12e$
49 $[49, 7, w^{3} - w^{2} - 6w + 3]$ $-2e^{3} + 12e$
53 $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ $-4e^{2} + 18$
53 $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ $-4e^{2} + 18$
59 $[59, 59, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2e^{2} - 6$
59 $[59, 59, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}2e^{2} - 6$
67 $[67, 67, 3w^{3} - 13w + 1]$ $\phantom{-}e^{3} - 5e$
67 $[67, 67, -w^{3} + w^{2} + 6w - 5]$ $\phantom{-}e^{3} - 5e$
81 $[81, 3, -3]$ $-4e^{2} + 22$
83 $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ $-2e^{2} + 6$
83 $[83, 83, 4w^{3} - 18w - 1]$ $-2e^{2} + 6$
89 $[89, 89, -2w^{3} + 10w + 1]$ $\phantom{-}2e^{3} - 16e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,w+1]$ $1$