Properties

Label 4.4.10025.1-20.3-c
Base field 4.4.10025.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20,10,-w - 2]$
Dimension $5$
CM no
Base change no

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Base field 4.4.10025.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 10x + 20\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[20,10,-w - 2]$
Dimension: $5$
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:

\(x^{5} - 2x^{4} - 15x^{3} + 28x^{2} + 48x - 80\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $-1$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $-\frac{1}{4}e^{4} + \frac{15}{4}e^{2} + \frac{1}{2}e - 11$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $-1$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{15}{4}e^{2} + 4e - 10$
19 $[19, 19, w - 1]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{15}{4}e^{2} - 4e + 10$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{15}{4}e^{2} + 6e - 12$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{15}{4}e^{2} - \frac{1}{2}e + 13$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{1}{2}e^{3} - \frac{33}{4}e^{2} + 4e + 15$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} - e + 10$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{7}{4}e^{2} + 5e$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $\phantom{-}e^{3} - e^{2} - 9e + 5$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $-\frac{1}{4}e^{4} - e^{3} + \frac{23}{4}e^{2} + \frac{15}{2}e - 27$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $\phantom{-}\frac{3}{4}e^{4} + \frac{1}{2}e^{3} - \frac{45}{4}e^{2} - 5e + 38$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $-\frac{3}{4}e^{4} + \frac{1}{2}e^{3} + \frac{37}{4}e^{2} - 4e - 22$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $-\frac{3}{4}e^{4} - \frac{1}{2}e^{3} + \frac{37}{4}e^{2} + 5e - 22$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{15}{2}e^{2} - \frac{5}{2}e - 25$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $-e^{2} - 2e + 15$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{7}{4}e^{2} + 5e - 2$
89 $[89, 89, w^{3} - 7w + 1]$ $-\frac{3}{4}e^{4} - \frac{3}{2}e^{3} + \frac{53}{4}e^{2} + 12e - 50$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w - 2]$ $1$
$5$ $[5,5,w^{3} + 2w^{2} - 7w - 9]$ $1$