Properties

Label 4.4.16400.1-19.1-f
Base field 4.4.16400.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, -w^{2} - w + 4]$
Dimension $13$
CM no
Base change no

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Base field 4.4.16400.1

Generator \(w\), with minimal polynomial \(x^{4} - 13x^{2} + 41\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19, 19, -w^{2} - w + 4]$
Dimension: $13$
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:

\(x^{13} + 2x^{12} - 24x^{11} - 54x^{10} + 193x^{9} + 507x^{8} - 546x^{7} - 1973x^{6} + 11x^{5} + 2772x^{4} + 1343x^{3} - 529x^{2} - 181x + 47\)

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Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + 2w^{2} + 6w - 11]$ $\phantom{-}e$
5 $[5, 5, -w - 2]$ $...$
5 $[5, 5, -w + 2]$ $...$
11 $[11, 11, -2w^{2} - w + 12]$ $...$
11 $[11, 11, 2w^{2} - w - 12]$ $...$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}1$
19 $[19, 19, w^{2} - w - 4]$ $...$
29 $[29, 29, -w - 1]$ $...$
29 $[29, 29, w - 1]$ $...$
31 $[31, 31, -2w^{2} - w + 14]$ $...$
31 $[31, 31, w^{3} - 3w^{2} - 6w + 19]$ $...$
31 $[31, 31, -w^{3} - 3w^{2} + 6w + 19]$ $...$
31 $[31, 31, -2w^{2} + w + 14]$ $...$
41 $[41, 41, -w]$ $...$
71 $[71, 71, w^{3} + 3w^{2} - 7w - 19]$ $...$
71 $[71, 71, w^{3} - 3w^{2} - 7w + 19]$ $...$
79 $[79, 79, w^{3} + 3w^{2} - 9w - 25]$ $...$
79 $[79, 79, w^{3} - 3w^{2} - 9w + 25]$ $...$
81 $[81, 3, -3]$ $...$
89 $[89, 89, -w^{3} - 4w^{2} + 6w + 24]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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