Properties

Label 4.4.7232.1-32.1-f
Base field 4.4.7232.1
Weight $[2, 2, 2, 2]$
Level norm $32$
Level $[32, 4, w^{3} - 3w^{2} - 2w + 4]$
Dimension $1$
CM no
Base change no

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Base field 4.4.7232.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[32, 4, w^{3} - 3w^{2} - 2w + 4]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$ $\phantom{-}0$
2 $[2, 2, -w - 1]$ $\phantom{-}1$
17 $[17, 17, w^{2} - w - 5]$ $-6$
17 $[17, 17, -\frac{1}{2}w^{3} + 2w^{2} + \frac{1}{2}w - 2]$ $-6$
23 $[23, 23, \frac{1}{2}w^{3} - 2w^{2} - \frac{1}{2}w + 4]$ $\phantom{-}0$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}0$
41 $[41, 41, -w^{3} + 3w^{2} + 2w - 7]$ $-6$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w]$ $-6$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ $-6$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w]$ $-6$
47 $[47, 47, \frac{3}{2}w^{3} - 4w^{2} - \frac{7}{2}w + 6]$ $\phantom{-}0$
47 $[47, 47, w^{3} - w^{2} - 4w - 1]$ $\phantom{-}0$
49 $[49, 7, w^{3} - 2w^{2} - 3w + 1]$ $-14$
49 $[49, 7, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w - 2]$ $-14$
71 $[71, 71, \frac{5}{2}w^{3} - 6w^{2} - \frac{17}{2}w + 12]$ $\phantom{-}0$
71 $[71, 71, 2w^{2} - 4w - 7]$ $\phantom{-}0$
73 $[73, 73, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}10$
73 $[73, 73, 2w - 1]$ $\phantom{-}10$
79 $[79, 79, \frac{3}{2}w^{3} - 4w^{2} - \frac{11}{2}w + 12]$ $\phantom{-}16$
79 $[79, 79, -w^{2} - w - 1]$ $-16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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