Properties

Label 4.4.2525.1-71.1-a
Base field 4.4.2525.1
Weight $[2, 2, 2, 2]$
Level norm $71$
Level $[71, 71, w^{3} + w^{2} - 4w - 6]$
Dimension $1$
CM no
Base change no

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Base field 4.4.2525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[71, 71, w^{3} + w^{2} - 4w - 6]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}2$
5 $[5, 5, w^{3} - 2w^{2} - 2w + 3]$ $-1$
11 $[11, 11, -w^{2} + 4]$ $-2$
11 $[11, 11, w^{2} - 2w - 3]$ $-5$
16 $[16, 2, 2]$ $-3$
29 $[29, 29, w^{3} - 4w - 1]$ $-8$
29 $[29, 29, w^{3} - 3w^{2} - w + 4]$ $\phantom{-}1$
41 $[41, 41, w^{3} - 2w^{2} - w + 4]$ $\phantom{-}7$
41 $[41, 41, -w^{3} + w^{2} + 2w + 2]$ $-5$
59 $[59, 59, -2w^{3} + 4w^{2} + 4w - 7]$ $\phantom{-}5$
59 $[59, 59, -3w^{2} + 2w + 7]$ $-4$
61 $[61, 61, -w^{3} + 4w^{2} - 6]$ $-5$
61 $[61, 61, w^{3} + w^{2} - 5w - 3]$ $-14$
71 $[71, 71, w^{3} + w^{2} - 4w - 6]$ $\phantom{-}1$
71 $[71, 71, 3w^{2} - 2w - 8]$ $\phantom{-}2$
71 $[71, 71, 3w^{2} - 4w - 7]$ $-10$
71 $[71, 71, w^{3} - 4w^{2} + w + 8]$ $-9$
79 $[79, 79, -2w^{3} + 3w^{2} + 5w - 2]$ $-8$
79 $[79, 79, 2w^{2} - 3w - 7]$ $-8$
79 $[79, 79, 2w^{2} - w - 8]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$71$ $[71, 71, w^{3} + w^{2} - 4w - 6]$ $-1$