Properties

Label 4.4.12725.1-16.1-d
Base field 4.4.12725.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $12$
CM no
Base change yes

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Base field 4.4.12725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $12$
CM: no
Base change: yes
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 7x^{11} - 45x^{10} + 350x^{9} + 392x^{8} - 4679x^{7} + 1153x^{6} + 20492x^{5} - 13640x^{4} - 28280x^{3} + 20368x^{2} + 6776x - 3632\)

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Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $...$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}e$
11 $[11, 11, w - 2]$ $...$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, w^{2} - 2w - 5]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
25 $[25, 5, -2w^{2} + 2w + 11]$ $...$
29 $[29, 29, w]$ $...$
29 $[29, 29, 2w^{2} - w - 10]$ $...$
29 $[29, 29, -2w^{2} + 3w + 9]$ $...$
29 $[29, 29, w - 1]$ $...$
31 $[31, 31, w^{3} - 6w - 6]$ $...$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $...$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $...$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $...$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $...$
59 $[59, 59, 2w^{2} - w - 13]$ $...$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $...$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$