Properties

Label 4.4.16448.1-20.1-a
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20, 10, -w^{3} + 3w^{2} + 4w - 2]$
Dimension $5$
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: $[20, 10, -w^{3} + 3w^{2} + 4w - 2]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 18x^{3} + 9x^{2} + 63x - 54\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $\phantom{-}e + 2$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $-\frac{1}{3}e^{4} - \frac{1}{3}e^{3} + 5e^{2} + 2e - 10$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $-\frac{1}{9}e^{4} - \frac{1}{3}e^{3} + e^{2} + 3e$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-\frac{1}{9}e^{4} - \frac{1}{3}e^{3} + 2e^{2} + 4e - 8$
25 $[25, 5, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{9}e^{4} - 2e^{2} + 6$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{1}{3}e^{3} - 4e^{2} - e + 4$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{3}e^{4} + e^{3} - 5e^{2} - 9e + 18$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $\phantom{-}\frac{1}{9}e^{4} - 2e^{2} - e + 10$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $-\frac{2}{9}e^{4} - \frac{1}{3}e^{3} + 3e^{2} + 4e - 4$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $\phantom{-}\frac{1}{9}e^{4} - \frac{1}{3}e^{3} - 2e^{2} + 3e + 2$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $\phantom{-}\frac{4}{9}e^{4} + \frac{1}{3}e^{3} - 7e^{2} - 4e + 18$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $-\frac{2}{9}e^{4} - \frac{1}{3}e^{3} + 3e^{2} + 4e - 4$
81 $[81, 3, -3]$ $\phantom{-}\frac{5}{9}e^{4} + \frac{4}{3}e^{3} - 9e^{2} - 13e + 28$
83 $[83, 83, -w - 3]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - 6e^{2} + 4e + 12$
83 $[83, 83, w^{2} - 3w - 7]$ $-\frac{7}{9}e^{4} - e^{3} + 12e^{2} + 7e - 30$
89 $[89, 89, w^{2} - 2w - 7]$ $\phantom{-}\frac{7}{9}e^{4} + \frac{4}{3}e^{3} - 13e^{2} - 12e + 38$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $-\frac{1}{9}e^{4} + \frac{1}{3}e^{3} + 3e^{2} - 2e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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