Properties

Label 4.4.14272.1-19.1-b
Base field 4.4.14272.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, -w^{2} + w + 4]$
Dimension $20$
CM no
Base change no

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Base field 4.4.14272.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[19, 19, -w^{2} + w + 4]$
Dimension: $20$
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:

\(x^{20} - 43x^{18} + 762x^{16} - 7243x^{14} + 40390x^{12} - 136052x^{10} + 274255x^{8} - 313426x^{6} + 177576x^{4} - 35924x^{2} + 2304\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $...$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $...$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $...$
13 $[13, 13, -w + 2]$ $...$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $...$
19 $[19, 19, -w^{2} + w + 4]$ $-1$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $...$
23 $[23, 23, w^{2} - 2w - 1]$ $...$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $...$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $...$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $...$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $...$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $...$
59 $[59, 59, w - 4]$ $...$
67 $[67, 67, 2w^{2} - 3w - 8]$ $...$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $...$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $...$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $...$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -w^{2} + w + 4]$ $1$