Properties

Label 4.4.16400.1-20.1-f
Base field 4.4.16400.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20, 10, w^{2} + w - 7]$
Dimension $4$
CM no
Base change no

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Base field 4.4.16400.1

Generator \(w\), with minimal polynomial \(x^{4} - 13x^{2} + 41\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[20, 10, w^{2} + w - 7]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 16x^{2} + 20\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + 2w^{2} + 6w - 11]$ $\phantom{-}1$
5 $[5, 5, -w - 2]$ $-1$
5 $[5, 5, -w + 2]$ $-1$
11 $[11, 11, -2w^{2} - w + 12]$ $\phantom{-}e$
11 $[11, 11, 2w^{2} - w - 12]$ $-\frac{1}{4}e^{3} + \frac{7}{2}e$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}\frac{1}{2}e^{3} - 7e$
19 $[19, 19, w^{2} - w - 4]$ $\phantom{-}e$
29 $[29, 29, -w - 1]$ $-\frac{1}{2}e^{2}$
29 $[29, 29, w - 1]$ $\phantom{-}e^{2} - 10$
31 $[31, 31, -2w^{2} - w + 14]$ $\phantom{-}\frac{1}{2}e^{3} - 7e$
31 $[31, 31, w^{3} - 3w^{2} - 6w + 19]$ $-2e$
31 $[31, 31, -w^{3} - 3w^{2} + 6w + 19]$ $-e$
31 $[31, 31, -2w^{2} + w + 14]$ $-\frac{1}{4}e^{3} + \frac{5}{2}e$
41 $[41, 41, -w]$ $-\frac{1}{2}e^{2} + 3$
71 $[71, 71, w^{3} + 3w^{2} - 7w - 19]$ $-\frac{3}{4}e^{3} + \frac{17}{2}e$
71 $[71, 71, w^{3} - 3w^{2} - 7w + 19]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{9}{2}e$
79 $[79, 79, w^{3} + 3w^{2} - 9w - 25]$ $-\frac{1}{4}e^{3} + \frac{1}{2}e$
79 $[79, 79, w^{3} - 3w^{2} - 9w + 25]$ $-\frac{3}{4}e^{3} + \frac{27}{2}e$
81 $[81, 3, -3]$ $-\frac{3}{2}e^{2} + 8$
89 $[89, 89, -w^{3} - 4w^{2} + 6w + 24]$ $-\frac{1}{2}e^{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{3} + 2w^{2} + 6w - 11]$ $-1$
$5$ $[5, 5, -w - 2]$ $1$