Properties

Label 4.4.14400.1-20.1-k
Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20, 10, \frac{2}{19}w^{3} - \frac{3}{19}w^{2} + \frac{1}{19}w - 1]$
Dimension $4$
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: $[20, 10, \frac{2}{19}w^{3} - \frac{3}{19}w^{2} + \frac{1}{19}w - 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 50x^{2} + 56x + 184\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ $\phantom{-}1$
5 $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ $\phantom{-}1$
5 $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ $-\frac{1}{172}e^{3} - \frac{7}{86}e^{2} + \frac{13}{86}e + \frac{77}{43}$
9 $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ $\phantom{-}\frac{1}{172}e^{3} + \frac{7}{86}e^{2} - \frac{13}{86}e - \frac{120}{43}$
19 $[19, 19, -w]$ $\phantom{-}e$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ $-\frac{1}{172}e^{3} - \frac{7}{86}e^{2} - \frac{73}{86}e + \frac{77}{43}$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ $\phantom{-}\frac{2}{43}e^{3} + \frac{13}{86}e^{2} - \frac{52}{43}e - \frac{57}{43}$
19 $[19, 19, w - 1]$ $-\frac{3}{86}e^{3} + \frac{1}{86}e^{2} + \frac{39}{43}e - \frac{54}{43}$
29 $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ $-\frac{7}{172}e^{3} - \frac{3}{43}e^{2} + \frac{91}{86}e + \frac{195}{43}$
29 $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ $\phantom{-}\frac{7}{172}e^{3} + \frac{3}{43}e^{2} - \frac{91}{86}e + \frac{192}{43}$
29 $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ $-\frac{1}{43}e^{3} + \frac{15}{86}e^{2} + \frac{69}{43}e - \frac{122}{43}$
29 $[29, 29, -w + 3]$ $\phantom{-}\frac{9}{172}e^{3} + \frac{10}{43}e^{2} - \frac{203}{86}e - \frac{48}{43}$
49 $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ $-\frac{21}{172}e^{3} - \frac{9}{43}e^{2} + \frac{359}{86}e + \frac{198}{43}$
49 $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ $\phantom{-}\frac{5}{43}e^{3} + \frac{11}{86}e^{2} - \frac{173}{43}e + \frac{266}{43}$
71 $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ $-\frac{13}{172}e^{3} + \frac{19}{43}e^{2} + \frac{341}{86}e - \frac{461}{43}$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ $\phantom{-}\frac{27}{172}e^{3} + \frac{30}{43}e^{2} - \frac{523}{86}e - \frac{316}{43}$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ $\phantom{-}\frac{11}{172}e^{3} - \frac{9}{86}e^{2} - \frac{229}{86}e + \frac{486}{43}$
71 $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ $-\frac{4}{43}e^{3} - \frac{13}{43}e^{2} + \frac{147}{43}e + \frac{415}{43}$
101 $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ $\phantom{-}\frac{2}{43}e^{3} + \frac{28}{43}e^{2} - \frac{95}{43}e - \frac{616}{43}$
101 $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ $\phantom{-}\frac{7}{43}e^{3} - \frac{19}{86}e^{2} - \frac{354}{43}e + \frac{338}{43}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ $-1$
$5$ $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ $-1$