Properties

Label 4.4.8112.1-9.1-e
Base field 4.4.8112.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, -w^{2} + 3]$
Dimension $2$
CM no
Base change no

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Base field 4.4.8112.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, -w^{2} + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 18\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
4 $[4, 2, w^{2} - w - 1]$ $\phantom{-}0$
9 $[9, 3, -w^{2} + 2]$ $-4$
13 $[13, 13, w^{3} - 4w + 2]$ $\phantom{-}e$
13 $[13, 13, -w^{3} + 4w + 2]$ $-e$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}e$
17 $[17, 17, -w^{3} + 3w - 1]$ $-e$
29 $[29, 29, w^{3} + w^{2} - 4w - 2]$ $-e$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}e$
43 $[43, 43, w^{2} + w - 4]$ $-8$
43 $[43, 43, w^{2} - w - 4]$ $-8$
53 $[53, 53, w^{3} - 2w - 2]$ $-12$
53 $[53, 53, -w^{3} + 2w - 2]$ $-12$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2e$
79 $[79, 79, -w^{3} - w^{2} + 4w + 1]$ $-2e$
101 $[101, 101, -w^{3} + w^{2} + 3w - 5]$ $\phantom{-}6$
101 $[101, 101, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}6$
103 $[103, 103, 2w^{2} - w - 4]$ $-4$
103 $[103, 103, 2w^{2} + w - 4]$ $-4$
107 $[107, 107, 2w^{2} + w - 5]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $-1$