Properties

Label 4.4.11197.1-29.2-a
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, w^{3} - 2w^{2} - 4w]$
Dimension $16$
CM no
Base change no

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Base field 4.4.11197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[29, 29, w^{3} - 2w^{2} - 4w]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} - 6x^{15} - 17x^{14} + 156x^{13} + 16x^{12} - 1518x^{11} + 1220x^{10} + 6856x^{9} - 8829x^{8} - 14254x^{7} + 24331x^{6} + 10272x^{5} - 27058x^{4} + 2034x^{3} + 8594x^{2} - 1364x - 562\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $...$
11 $[11, 11, -w - 2]$ $...$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $...$
13 $[13, 13, -w^{2} + 2w + 2]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $...$
23 $[23, 23, -w^{2} + w + 3]$ $...$
23 $[23, 23, -w^{2} + 3]$ $...$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $...$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $...$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $-1$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $...$
47 $[47, 47, w^{2} - 3w - 2]$ $...$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $...$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $...$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $...$
83 $[83, 83, -2w + 3]$ $...$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $...$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w^{3} - 2w^{2} - 4w]$ $1$