Properties

Base field 4.4.4752.1
Weight [2, 2, 2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 4.4.4752.1-1.1-a
Dimension 2
CM yes
Base change yes

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Base field 4.4.4752.1

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

Form

Weight [2, 2, 2, 2]
Level $[1, 1, 1]$
Label 4.4.4752.1-1.1-a
Dimension 2
Is CM yes
Is base change yes
Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 1]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + w^{2} + 3w]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}0$
13 $[13, 13, w^{3} - 2w^{2} - w + 1]$ $-2e$
13 $[13, 13, w^{3} - w^{2} - 2w + 1]$ $-2e$
23 $[23, 23, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}0$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}0$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}0$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}0$
59 $[59, 59, w^{2} - 5]$ $\phantom{-}0$
59 $[59, 59, w^{2} - 2w - 4]$ $\phantom{-}0$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}4e - 6$
61 $[61, 61, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}4e - 6$
71 $[71, 71, w^{3} - w^{2} - 2w - 2]$ $\phantom{-}0$
71 $[71, 71, -w^{3} + 2w^{2} + w - 4]$ $\phantom{-}0$
73 $[73, 73, 2w^{2} - w - 5]$ $-2e + 12$
73 $[73, 73, w^{3} - 2w^{2} - 2w + 6]$ $-2e + 12$
83 $[83, 83, -2w^{3} + 3w^{2} + 6w - 6]$ $\phantom{-}0$
83 $[83, 83, -2w^{3} + 4w^{2} + 5w - 5]$ $\phantom{-}0$
83 $[83, 83, -2w^{3} + 2w^{2} + 7w - 2]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).