Properties

Label 4.4.11025.1-16.2-d
Base field \(\Q(\sqrt{5}, \sqrt{21})\)
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 4, -w]$
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: $[16, 4, -w]$
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:

\(x^{4} - 6x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{11}{4}w + 5]$ $\phantom{-}0$
4 $[4, 2, \frac{1}{8}w^{3} - \frac{1}{2}w^{2} - \frac{5}{8}w + \frac{3}{2}]$ $-2$
5 $[5, 5, -\frac{3}{8}w^{3} + \frac{35}{8}w - \frac{1}{2}]$ $\phantom{-}e$
5 $[5, 5, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{1}{2}]$ $-\frac{1}{2}e^{3} + 3e$
9 $[9, 3, -\frac{1}{8}w^{3} + \frac{17}{8}w + \frac{3}{2}]$ $-3$
41 $[41, 41, \frac{1}{8}w^{3} - \frac{1}{8}w + \frac{3}{2}]$ $\phantom{-}\frac{3}{2}e^{3} - 8e$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{3}{2}]$ $-e^{3} + e$
41 $[41, 41, \frac{3}{8}w^{3} - \frac{35}{8}w - \frac{3}{2}]$ $\phantom{-}\frac{5}{2}e^{3} - 13e$
41 $[41, 41, -\frac{1}{8}w^{3} + \frac{1}{8}w + \frac{3}{2}]$ $-\frac{1}{2}e^{3}$
49 $[49, 7, \frac{1}{8}w^{3} - \frac{17}{8}w + \frac{7}{2}]$ $\phantom{-}4$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w - \frac{5}{2}]$ $\phantom{-}4e^{3} - 19e$
59 $[59, 59, -\frac{7}{8}w^{3} + \frac{3}{2}w^{2} + \frac{83}{8}w - \frac{35}{2}]$ $-\frac{3}{2}e^{3} + 11e$
59 $[59, 59, -\frac{3}{4}w^{3} + \frac{3}{2}w^{2} + \frac{33}{4}w - 16]$ $-e^{3} + 9e$
59 $[59, 59, \frac{5}{8}w^{3} - \frac{53}{8}w + \frac{5}{2}]$ $-\frac{5}{2}e^{3} + 7e$
79 $[79, 79, \frac{3}{8}w^{3} - w^{2} - \frac{35}{8}w + \frac{21}{2}]$ $-3e^{2} + 7$
79 $[79, 79, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 5]$ $-3e^{2} + 7$
79 $[79, 79, \frac{7}{8}w^{3} - \frac{79}{8}w - \frac{1}{2}]$ $\phantom{-}3e^{2} - 11$
79 $[79, 79, -\frac{3}{8}w^{3} - w^{2} + \frac{35}{8}w + \frac{21}{2}]$ $\phantom{-}3e^{2} - 11$
89 $[89, 89, \frac{1}{8}w^{3} - \frac{1}{8}w - \frac{5}{2}]$ $-5e^{3} + 21e$
89 $[89, 89, \frac{3}{8}w^{3} - \frac{35}{8}w + \frac{5}{2}]$ $-\frac{1}{2}e^{3} - 2e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{4}w^{3}-\frac{1}{2}w^{2}-\frac{11}{4}w+5]$ $-1$