Properties

Label 4.4.11025.1-16.3-e
Base field \(\Q(\sqrt{5}, \sqrt{21})\)
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16,4,\frac{1}{4}w^{3} - \frac{13}{4}w]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{5}, \sqrt{21})\)

Generator \(w\), with minimal polynomial \(x^{4} - 13x^{2} + 16\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16,4,\frac{1}{4}w^{3} - \frac{13}{4}w]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $13$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 18x^{2} + 36\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{11}{4}w + 5]$ $\phantom{-}2$
4 $[4, 2, \frac{1}{8}w^{3} - \frac{1}{2}w^{2} - \frac{5}{8}w + \frac{3}{2}]$ $\phantom{-}0$
5 $[5, 5, -\frac{3}{8}w^{3} + \frac{35}{8}w - \frac{1}{2}]$ $\phantom{-}e$
5 $[5, 5, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{1}{2}]$ $-\frac{1}{6}e^{3} + 3e$
9 $[9, 3, -\frac{1}{8}w^{3} + \frac{17}{8}w + \frac{3}{2}]$ $\phantom{-}1$
41 $[41, 41, \frac{1}{8}w^{3} - \frac{1}{8}w + \frac{3}{2}]$ $\phantom{-}\frac{1}{6}e^{3} - e$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{3}{2}]$ $-\frac{1}{6}e^{3}$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{3}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
41 $[41, 41, -\frac{1}{8}w^{3} + \frac{1}{8}w + \frac{3}{2}]$ $-\frac{1}{3}e^{3} + 5e$
49 $[49, 7, \frac{1}{8}w^{3} - \frac{17}{8}w + \frac{7}{2}]$ $\phantom{-}8$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w - \frac{5}{2}]$ $\phantom{-}\frac{1}{6}e^{3} - e$
59 $[59, 59, -\frac{7}{8}w^{3} + \frac{3}{2}w^{2} + \frac{83}{8}w - \frac{35}{2}]$ $-\frac{2}{3}e^{3} + 9e$
59 $[59, 59, -\frac{3}{4}w^{3} + \frac{3}{2}w^{2} + \frac{33}{4}w - 16]$ $\phantom{-}\frac{1}{2}e^{3} - 5e$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w + \frac{5}{2}]$ $-\frac{1}{3}e^{3} + 5e$
79 $[79, 79, \frac{3}{8}w^{3} - w^{2} - \frac{35}{8}w + \frac{21}{2}]$ $-e^{2} + 17$
79 $[79, 79, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 5]$ $-e^{2} + 5$
79 $[79, 79, \frac{7}{8}w^{3} - \frac{79}{8}w - \frac{1}{2}]$ $\phantom{-}e^{2} - 13$
79 $[79, 79, -\frac{3}{8}w^{3} - w^{2} + \frac{35}{8}w + \frac{21}{2}]$ $\phantom{-}e^{2} - 1$
89 $[89, 89, \frac{1}{8}w^{3} - \frac{1}{8}w - \frac{5}{2}]$ $\phantom{-}\frac{7}{6}e^{3} - 14e$
89 $[89, 89, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{5}{2}]$ $\phantom{-}\frac{1}{3}e^{3} - 7e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,-\frac{1}{8}w^{3} + \frac{1}{2}w^{2} + \frac{5}{8}w - \frac{3}{2}]$ $1$