Properties

Label 4.4.12725.1-29.1-b
Base field 4.4.12725.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, w]$
Dimension $19$
CM no
Base change no

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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: $[29, 29, w]$
Dimension: $19$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{19} - 16x^{18} + 11x^{17} + 1030x^{16} - 4177x^{15} - 22127x^{14} + 149213x^{13} + 127780x^{12} - 2248324x^{11} + 1702099x^{10} + 15939357x^{9} - 27900465x^{8} - 44352715x^{7} + 137094509x^{6} - 15953436x^{5} - 219543048x^{4} + 188768667x^{3} + 17947097x^{2} - 72528926x + 20930191\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{2} - 5]$ $...$
11 $[11, 11, -w^{2} + 2w + 4]$ $...$
11 $[11, 11, w - 2]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, w^{2} - 2w - 5]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
25 $[25, 5, -2w^{2} + 2w + 11]$ $...$
29 $[29, 29, w]$ $-1$
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
$29$ $[29, 29, w]$ $1$