Properties

Label 4.4.16448.1-5.2-a
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $5$
Level $[5, 5, w - 1]$
Dimension $8$
CM no
Base change no

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Base field 4.4.16448.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[5, 5, w - 1]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 32x^{6} + 304x^{4} - 768x^{2} + 256\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-\frac{1}{128}e^{7} + \frac{7}{32}e^{5} - \frac{13}{8}e^{3} + 2e$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-1$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $-\frac{1}{16}e^{5} + \frac{5}{4}e^{3} - 4e$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{64}e^{7} - \frac{7}{16}e^{5} + \frac{15}{4}e^{3} - 10e$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $-\frac{1}{32}e^{7} + e^{5} - 9e^{3} + 16e$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-\frac{1}{32}e^{6} + \frac{3}{4}e^{4} - 5e^{2} + 10$
25 $[25, 5, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 10e$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $-\frac{1}{32}e^{7} + e^{5} - 9e^{3} + 17e$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{64}e^{7} - \frac{1}{2}e^{5} + 5e^{3} - 14e$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $-\frac{1}{32}e^{6} + e^{4} - 8e^{2} + 6$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $\phantom{-}\frac{1}{16}e^{5} - \frac{5}{4}e^{3} + 6e$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $-\frac{1}{32}e^{6} + \frac{1}{2}e^{4} - 2e^{2} + 14$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $-\frac{1}{32}e^{7} + e^{5} - 10e^{3} + 28e$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $-\frac{1}{2}e^{4} + 8e^{2} - 16$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{3}{2}e^{4} + 8e^{2} + 2$
83 $[83, 83, -w - 3]$ $-\frac{3}{32}e^{6} + \frac{9}{4}e^{4} - 14e^{2} + 14$
83 $[83, 83, w^{2} - 3w - 7]$ $\phantom{-}\frac{1}{16}e^{6} - 2e^{4} + 17e^{2} - 20$
89 $[89, 89, w^{2} - 2w - 7]$ $-\frac{1}{2}e^{4} + 8e^{2} - 18$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $-\frac{3}{64}e^{7} + \frac{21}{16}e^{5} - \frac{41}{4}e^{3} + 14e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w - 1]$ $1$