Properties

Label 4.4.17069.1-16.1-f
Base field 4.4.17069.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $12$
CM no
Base change no

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Base field 4.4.17069.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} - 4x + 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 6x^{11} - 12x^{10} + 125x^{9} - 34x^{8} - 904x^{7} + 915x^{6} + 2606x^{5} - 3596x^{4} - 2445x^{3} + 4023x^{2} + 609x - 1273\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $...$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $...$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $...$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $...$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $...$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $...$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $...$
25 $[25, 5, w^{2} - 2w - 7]$ $...$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $...$
29 $[29, 29, w - 2]$ $...$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $...$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $...$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $...$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $...$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $...$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $...$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $...$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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