Properties

Label 4.4.14400.1-19.3-a
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

Related objects

Downloads

Learn more about

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:

\(x^{8} - 32x^{6} + 334x^{4} - 1143x^{2} + 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ $\phantom{-}\frac{4}{39}e^{6} - \frac{31}{13}e^{4} + \frac{532}{39}e^{2} - \frac{112}{39}$
5 $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ $-\frac{7}{351}e^{7} + \frac{10}{13}e^{5} - \frac{3310}{351}e^{3} + \frac{12754}{351}e$
5 $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ $\phantom{-}e$
9 $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ $-\frac{19}{351}e^{6} + \frac{16}{13}e^{4} - \frac{2215}{351}e^{2} - \frac{482}{351}$
19 $[19, 19, -w]$ $-\frac{44}{351}e^{6} + \frac{35}{13}e^{4} - \frac{4760}{351}e^{2} - \frac{211}{351}$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ $\phantom{-}\frac{61}{351}e^{6} - \frac{50}{13}e^{4} + \frac{6982}{351}e^{2} + \frac{2231}{351}$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ $-1$
19 $[19, 19, w - 1]$ $\phantom{-}\frac{61}{351}e^{6} - \frac{50}{13}e^{4} + \frac{6982}{351}e^{2} + \frac{2231}{351}$
29 $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ $-\frac{31}{351}e^{7} + \frac{35}{13}e^{5} - \frac{9193}{351}e^{3} + \frac{28402}{351}e$
29 $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ $\phantom{-}\frac{4}{27}e^{7} - 4e^{5} + \frac{877}{27}e^{3} - \frac{2050}{27}e$
29 $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ $\phantom{-}\frac{23}{351}e^{7} - \frac{18}{13}e^{5} + \frac{1850}{351}e^{3} + \frac{5830}{351}e$
29 $[29, 29, -w + 3]$ $-\frac{8}{117}e^{7} + \frac{25}{13}e^{5} - \frac{1961}{117}e^{3} + \frac{5333}{117}e$
49 $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ $\phantom{-}\frac{110}{351}e^{6} - \frac{94}{13}e^{4} + \frac{14357}{351}e^{2} - \frac{2456}{351}$
49 $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ $-\frac{148}{351}e^{6} + \frac{126}{13}e^{4} - \frac{18787}{351}e^{2} + \frac{1141}{351}$
71 $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ $\phantom{-}\frac{4}{39}e^{7} - \frac{31}{13}e^{5} + \frac{571}{39}e^{3} - \frac{580}{39}e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ $-\frac{58}{351}e^{7} + \frac{55}{13}e^{5} - \frac{11029}{351}e^{3} + \frac{21085}{351}e$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ $\phantom{-}\frac{7}{351}e^{7} + \frac{3}{13}e^{5} - \frac{4412}{351}e^{3} + \frac{27260}{351}e$
71 $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ $-\frac{7}{351}e^{7} - \frac{3}{13}e^{5} + \frac{4763}{351}e^{3} - \frac{31472}{351}e$
101 $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ $-\frac{8}{117}e^{7} + \frac{25}{13}e^{5} - \frac{2078}{117}e^{3} + \frac{6971}{117}e$
101 $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ $-\frac{62}{351}e^{7} + \frac{70}{13}e^{5} - \frac{18035}{351}e^{3} + \frac{52943}{351}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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