Properties

Label 4.4.2000.1-320.1-g
Base field \(\Q(\zeta_{20})^+\)
Weight $[2, 2, 2, 2]$
Level norm $320$
Level $[320, 20, -2w^{3} - 4w^{2} + 8w + 10]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\zeta_{20})^+\)

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[320, 20, -2w^{3} - 4w^{2} + 8w + 10]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{3} - w^{2} + 3w + 4]$ $\phantom{-}0$
5 $[5, 5, w]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}4$
19 $[19, 19, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}4$
19 $[19, 19, -w^{3} - w^{2} + 3w + 1]$ $\phantom{-}4$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}4$
41 $[41, 41, w + 3]$ $-6$
41 $[41, 41, -w^{3} + 3w + 3]$ $-6$
41 $[41, 41, -w^{3} + 3w - 3]$ $-6$
41 $[41, 41, w - 3]$ $-6$
59 $[59, 59, 2w^{2} + w - 7]$ $-4$
59 $[59, 59, -w^{3} - 2w^{2} + 3w + 3]$ $-4$
59 $[59, 59, 2w^{3} - w^{2} - 7w + 2]$ $-4$
59 $[59, 59, w^{3} - w^{2} - w + 3]$ $-4$
61 $[61, 61, 3w^{2} - w - 8]$ $-2$
61 $[61, 61, w^{3} + 3w^{2} - 3w - 7]$ $-2$
61 $[61, 61, -w^{3} + 3w^{2} + 3w - 7]$ $-2$
61 $[61, 61, -3w^{2} - w + 8]$ $-2$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}0$
79 $[79, 79, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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