Properties

Label 4.4.7232.1-16.2-b
Base field 4.4.7232.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 4, w^{2} - 2w - 4]$
Dimension $3$
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: $[16, 4, w^{2} - 2w - 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - x^{2} - 4x + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$ $\phantom{-}0$
2 $[2, 2, -w - 1]$ $\phantom{-}e$
17 $[17, 17, w^{2} - w - 5]$ $\phantom{-}e^{2} + e - 2$
17 $[17, 17, -\frac{1}{2}w^{3} + 2w^{2} + \frac{1}{2}w - 2]$ $\phantom{-}e^{2} + e - 2$
23 $[23, 23, \frac{1}{2}w^{3} - 2w^{2} - \frac{1}{2}w + 4]$ $\phantom{-}2e^{2} - 2e - 4$
23 $[23, 23, -w^{2} + w + 3]$ $-2e^{2} + 2e + 4$
41 $[41, 41, -w^{3} + 3w^{2} + 2w - 7]$ $-3e^{2} + e + 10$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w]$ $-3e^{2} + e + 10$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ $\phantom{-}2e + 4$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w]$ $\phantom{-}2e + 4$
47 $[47, 47, \frac{3}{2}w^{3} - 4w^{2} - \frac{7}{2}w + 6]$ $\phantom{-}2e^{2} + 2e - 8$
47 $[47, 47, w^{3} - w^{2} - 4w - 1]$ $-2e^{2} - 2e + 8$
49 $[49, 7, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}3e^{2} - e - 14$
49 $[49, 7, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w - 2]$ $-3e^{2} + e + 2$
71 $[71, 71, \frac{5}{2}w^{3} - 6w^{2} - \frac{17}{2}w + 12]$ $\phantom{-}4e - 4$
71 $[71, 71, 2w^{2} - 4w - 7]$ $-4e + 4$
73 $[73, 73, -w^{3} + 2w^{2} + 5w - 3]$ $-e^{2} - e - 2$
73 $[73, 73, 2w - 1]$ $-e^{2} - e - 2$
79 $[79, 79, \frac{3}{2}w^{3} - 4w^{2} - \frac{11}{2}w + 12]$ $-2e^{2} + 6e$
79 $[79, 79, -w^{2} - w - 1]$ $\phantom{-}2e^{2} - 6e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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