Properties

Label 4.4.10025.1-16.1-b
Base field 4.4.10025.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $1$
CM no
Base change yes

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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: $[16, 2, 2]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $13$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $-1$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $-1$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $\phantom{-}4$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $\phantom{-}4$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $\phantom{-}0$
19 $[19, 19, w - 1]$ $\phantom{-}0$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $-2$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $-2$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $\phantom{-}10$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}10$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}0$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $\phantom{-}0$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $-2$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $-2$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $-12$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $-12$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $\phantom{-}0$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $\phantom{-}0$
81 $[81, 3, -3]$ $\phantom{-}8$
89 $[89, 89, w^{3} - 7w + 1]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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