Properties

Label 4.4.12400.1-20.2-b
Base field 4.4.12400.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20,10,\frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{7}{2}]$
Dimension $1$
CM no
Base change no

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Base field 4.4.12400.1

Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 31\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[20,10,\frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{7}{2}]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ $-1$
5 $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ $\phantom{-}1$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ $\phantom{-}1$
9 $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ $\phantom{-}1$
19 $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ $-8$
19 $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ $\phantom{-}1$
29 $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ $\phantom{-}9$
29 $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ $-9$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-7$
59 $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ $\phantom{-}0$
59 $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ $\phantom{-}12$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ $-11$
61 $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ $\phantom{-}1$
71 $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ $\phantom{-}0$
71 $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ $\phantom{-}0$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ $-10$
79 $[79, 79, -2w^{2} + w + 10]$ $\phantom{-}1$
79 $[79, 79, 2w^{2} + w - 10]$ $\phantom{-}7$
79 $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ $\phantom{-}5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{11}{2}]$ $1$
$5$ $[5,5,\frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 4]$ $-1$