Properties

Label 4.4.12400.1-16.1-d
Base field 4.4.12400.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $8$
CM no
Base change yes

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Base field 4.4.12400.1

Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 31\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $8$
CM: no
Base change: yes
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 30x^{6} + 260x^{4} - 600x^{2} + 400\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ $\phantom{-}\frac{3}{50}e^{7} - \frac{17}{10}e^{5} + \frac{64}{5}e^{3} - 15e$
9 $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ $\phantom{-}\frac{3}{50}e^{7} - \frac{17}{10}e^{5} + \frac{64}{5}e^{3} - 15e$
19 $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ $-\frac{1}{25}e^{7} + \frac{11}{10}e^{5} - \frac{41}{5}e^{3} + 12e$
19 $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ $-\frac{1}{25}e^{7} + \frac{11}{10}e^{5} - \frac{41}{5}e^{3} + 12e$
29 $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ $\phantom{-}\frac{1}{10}e^{6} - \frac{13}{5}e^{4} + 17e^{2} - 14$
29 $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ $\phantom{-}\frac{1}{10}e^{6} - \frac{13}{5}e^{4} + 17e^{2} - 14$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-\frac{9}{50}e^{7} + \frac{26}{5}e^{5} - \frac{202}{5}e^{3} + 52e$
59 $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ $-\frac{1}{5}e^{6} + 6e^{4} - 48e^{2} + 60$
59 $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ $-\frac{1}{5}e^{6} + 6e^{4} - 48e^{2} + 60$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ $\phantom{-}\frac{2}{25}e^{7} - \frac{12}{5}e^{5} + \frac{97}{5}e^{3} - 27e$
61 $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ $\phantom{-}\frac{2}{25}e^{7} - \frac{12}{5}e^{5} + \frac{97}{5}e^{3} - 27e$
71 $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ $\phantom{-}\frac{1}{10}e^{7} - \frac{14}{5}e^{5} + 20e^{3} - 16e$
71 $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ $\phantom{-}\frac{1}{10}e^{7} - \frac{14}{5}e^{5} + 20e^{3} - 16e$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ $-\frac{9}{50}e^{7} + 5e^{5} - \frac{182}{5}e^{3} + 40e$
79 $[79, 79, -2w^{2} + w + 10]$ $-\frac{1}{10}e^{6} + 3e^{4} - 24e^{2} + 32$
79 $[79, 79, 2w^{2} + w - 10]$ $-\frac{1}{10}e^{6} + 3e^{4} - 24e^{2} + 32$
79 $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ $-\frac{9}{50}e^{7} + 5e^{5} - \frac{182}{5}e^{3} + 40e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,-\frac{1}{2}w^{3}-\frac{1}{2}w^{2}+\frac{7}{2}w+\frac{11}{2}]$ $1$