Properties

Label 4.4.10025.1-20.4-d
Base field 4.4.10025.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20,10,\frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 9]$
Dimension $1$
CM no
Base change no

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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: $[20,10,\frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 9]$
Dimension: $1$
CM: no
Base change: no
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 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $\phantom{-}2$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $-1$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $\phantom{-}0$
19 $[19, 19, w - 1]$ $\phantom{-}4$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $\phantom{-}0$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $\phantom{-}4$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $\phantom{-}2$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}10$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}4$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $\phantom{-}4$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $\phantom{-}14$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $-6$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $-12$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $\phantom{-}16$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $-12$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $\phantom{-}4$
81 $[81, 3, -3]$ $-14$
89 $[89, 89, w^{3} - 7w + 1]$ $\phantom{-}2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,-\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 4]$ $1$
$5$ $[5,5,w^{3} + 2w^{2} - 7w - 9]$ $1$