Properties

Base field 4.4.8768.1
Weight [2, 2, 2, 2]
Level norm 16
Level $[16, 2, 2]$
Label 4.4.8768.1-16.1-a
Dimension 2
CM no
Base change no

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Base field 4.4.8768.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[16, 2, 2]$
Label 4.4.8768.1-16.1-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 4x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}0$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-\frac{1}{2}e + \frac{5}{2}$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}\frac{1}{2}e - \frac{9}{2}$
7 $[7, 7, w - 1]$ $-3$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e + \frac{3}{2}$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{5}{2}e + \frac{5}{2}$
31 $[31, 31, w^{2} - 5]$ $-3e + 6$
31 $[31, 31, -w^{2} + 2w + 4]$ $-5$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}2e + 1$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $-5$
47 $[47, 47, w^{2} - 2w - 5]$ $\phantom{-}\frac{3}{2}e - \frac{13}{2}$
47 $[47, 47, w^{2} - 6]$ $-\frac{1}{2}e - \frac{5}{2}$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-1$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-e - 4$
79 $[79, 79, -w - 3]$ $\phantom{-}\frac{3}{2}e - \frac{23}{2}$
79 $[79, 79, w - 4]$ $-\frac{7}{2}e + \frac{7}{2}$
81 $[81, 3, -3]$ $\phantom{-}e - 10$
89 $[89, 89, w^{2} - 3w - 2]$ $-\frac{11}{2}e + \frac{15}{2}$
89 $[89, 89, w^{2} + w - 4]$ $-\frac{3}{2}e - \frac{1}{2}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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