Properties

Label 4.4.16609.1-4.1-a
Base field 4.4.16609.1
Weight $[2, 2, 2, 2]$
Level norm $4$
Level $[4, 4, w + 1]$
Dimension $2$
CM no
Base change no

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Base field 4.4.16609.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[4, 4, w + 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} + x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $\phantom{-}0$
3 $[3, 3, -w^{2} + w + 3]$ $-1$
5 $[5, 5, w^{2} - 4]$ $\phantom{-}e$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $-e - 3$
17 $[17, 17, -w^{2} + w + 5]$ $-3e$
27 $[27, 3, -w^{3} + 4w - 2]$ $\phantom{-}3e + 5$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}5e + 3$
29 $[29, 29, -w^{3} + 4w + 2]$ $\phantom{-}3$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $\phantom{-}e - 5$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $-4e - 3$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $-3e - 5$
61 $[61, 61, w^{2} - 2w - 2]$ $-2e - 5$
61 $[61, 61, 2w^{2} - w - 8]$ $-2e - 8$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $\phantom{-}e + 1$
73 $[73, 73, -w^{2} - 2w + 2]$ $\phantom{-}5e + 5$
79 $[79, 79, w^{2} - 2w - 4]$ $-2e - 4$
89 $[89, 89, w^{2} + w - 5]$ $\phantom{-}2e - 3$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $-5e - 3$
89 $[89, 89, w^{3} - 5w - 5]$ $\phantom{-}3e + 9$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}2e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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