Properties

Label 4.4.14400.1-16.1-e
Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
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: $[16, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $23$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 4x^{3} - 28x^{2} + 16x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 3]$ $\phantom{-}0$
5 $[5, 5, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{27}{19}w - 1]$ $\phantom{-}\frac{1}{24}e^{3} + \frac{1}{3}e^{2} - \frac{1}{3}e + \frac{1}{3}$
5 $[5, 5, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{8}{19}w - 2]$ $\phantom{-}\frac{1}{24}e^{3} + \frac{1}{3}e^{2} - \frac{1}{3}e - \frac{11}{3}$
9 $[9, 3, -\frac{2}{19}w^{3} + \frac{3}{19}w^{2} + \frac{37}{19}w - 4]$ $-2$
19 $[19, 19, -w]$ $\phantom{-}e$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 1]$ $-\frac{1}{12}e^{3} - \frac{2}{3}e^{2} - \frac{1}{3}e + \frac{4}{3}$
19 $[19, 19, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e^{2} - \frac{23}{3}e - \frac{4}{3}$
19 $[19, 19, w - 1]$ $-\frac{1}{4}e^{3} - e^{2} + 7e - 4$
29 $[29, 29, -\frac{5}{19}w^{3} - \frac{2}{19}w^{2} + \frac{64}{19}w + 2]$ $-\frac{7}{24}e^{3} - \frac{11}{6}e^{2} + \frac{10}{3}e + \frac{17}{3}$
29 $[29, 29, \frac{10}{19}w^{3} - \frac{34}{19}w^{2} - \frac{71}{19}w + 9]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{1}{2}e^{2} - 2e + 5$
29 $[29, 29, \frac{4}{19}w^{3} - \frac{6}{19}w^{2} - \frac{55}{19}w + 4]$ $\phantom{-}\frac{3}{8}e^{3} + \frac{3}{2}e^{2} - 10e + 3$
29 $[29, 29, -w + 3]$ $-\frac{13}{24}e^{3} - \frac{17}{6}e^{2} + \frac{34}{3}e - \frac{1}{3}$
49 $[49, 7, \frac{5}{19}w^{3} - \frac{17}{19}w^{2} - \frac{64}{19}w + 11]$ $\phantom{-}\frac{1}{4}e^{3} + e^{2} - 8e - 2$
49 $[49, 7, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{92}{19}w - 1]$ $-\frac{1}{4}e^{3} - e^{2} + 8e - 6$
71 $[71, 71, \frac{3}{19}w^{3} + \frac{5}{19}w^{2} - \frac{46}{19}w - 1]$ $-\frac{7}{12}e^{3} - \frac{8}{3}e^{2} + \frac{44}{3}e - \frac{2}{3}$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w]$ $\phantom{-}\frac{7}{12}e^{3} + \frac{8}{3}e^{2} - \frac{44}{3}e + \frac{14}{3}$
71 $[71, 71, \frac{6}{19}w^{3} - \frac{9}{19}w^{2} - \frac{73}{19}w + 4]$ $\phantom{-}\frac{1}{12}e^{3} + \frac{2}{3}e^{2} + \frac{4}{3}e - \frac{10}{3}$
71 $[71, 71, -\frac{3}{19}w^{3} + \frac{14}{19}w^{2} + \frac{27}{19}w - 3]$ $-\frac{1}{12}e^{3} - \frac{2}{3}e^{2} - \frac{4}{3}e - \frac{2}{3}$
101 $[101, 101, \frac{7}{19}w^{3} - \frac{1}{19}w^{2} - \frac{63}{19}w - 3]$ $-\frac{11}{24}e^{3} - \frac{8}{3}e^{2} + \frac{23}{3}e - \frac{5}{3}$
101 $[101, 101, -\frac{9}{19}w^{3} + \frac{23}{19}w^{2} + \frac{81}{19}w - 5]$ $\phantom{-}\frac{5}{24}e^{3} + \frac{2}{3}e^{2} - \frac{17}{3}e + \frac{35}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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