Properties

Label 4.4.14400.1-19.3-c
Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,-\frac{4}{19}w^{3} + \frac{6}{19}w^{2} + \frac{55}{19}w - 2]$
Dimension $8$
CM no
Base change no

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Base field \(\Q(\sqrt{5}, \sqrt{6})\)

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19,19,-\frac{4}{19}w^{3} + \frac{6}{19}w^{2} + \frac{55}{19}w - 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 14x^{6} + 58x^{4} - 63x^{2} + 13\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ $\phantom{-}\frac{2}{13}e^{6} - \frac{21}{13}e^{4} + \frac{62}{13}e^{2} - 4$
5 $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ $-\frac{3}{13}e^{7} + \frac{38}{13}e^{5} - \frac{132}{13}e^{3} + 6e$
5 $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ $\phantom{-}e$
9 $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ $\phantom{-}\frac{1}{13}e^{6} - \frac{4}{13}e^{4} - \frac{21}{13}e^{2} + 2$
19 $[19, 19, -w]$ $\phantom{-}e^{4} - 8e^{2} + 7$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ $\phantom{-}\frac{5}{13}e^{6} - \frac{72}{13}e^{4} + \frac{272}{13}e^{2} - 13$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ $\phantom{-}1$
19 $[19, 19, w - 1]$ $-\frac{5}{13}e^{6} + \frac{46}{13}e^{4} - \frac{90}{13}e^{2} + 1$
29 $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ $\phantom{-}\frac{11}{13}e^{7} - \frac{135}{13}e^{5} + \frac{471}{13}e^{3} - 28e$
29 $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ $\phantom{-}e^{3} - 8e$
29 $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ $\phantom{-}\frac{5}{13}e^{7} - \frac{72}{13}e^{5} + \frac{272}{13}e^{3} - 10e$
29 $[29, 29, -w + 3]$ $-\frac{6}{13}e^{7} + \frac{63}{13}e^{5} - \frac{173}{13}e^{3} + 7e$
49 $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ $-\frac{8}{13}e^{6} + \frac{84}{13}e^{4} - \frac{235}{13}e^{2} + 12$
49 $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ $-\frac{8}{13}e^{6} + \frac{84}{13}e^{4} - \frac{209}{13}e^{2} - 1$
71 $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ $-\frac{2}{13}e^{7} + \frac{21}{13}e^{5} - \frac{75}{13}e^{3} + 14e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ $\phantom{-}\frac{4}{13}e^{7} - \frac{29}{13}e^{5} + \frac{7}{13}e^{3} + 7e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ $-\frac{7}{13}e^{7} + \frac{93}{13}e^{5} - \frac{334}{13}e^{3} + 16e$
71 $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ $\phantom{-}\frac{1}{13}e^{7} - \frac{17}{13}e^{5} + \frac{57}{13}e^{3} + 2e$
101 $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ $-\frac{2}{13}e^{7} + \frac{47}{13}e^{5} - \frac{296}{13}e^{3} + 33e$
101 $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ $\phantom{-}\frac{2}{13}e^{7} - \frac{8}{13}e^{5} - \frac{81}{13}e^{3} + 25e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-\frac{4}{19}w^{3} + \frac{6}{19}w^{2} + \frac{55}{19}w - 2]$ $-1$