Properties

Label 4.4.9792.1-1.1-a
Base field 4.4.9792.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $4$
CM no
Base change yes

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Base field 4.4.9792.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $4$
CM: no
Base change: yes
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 4x^{3} - 28x^{2} + 64x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{12}{7}e + \frac{20}{7}$
7 $[7, 7, w]$ $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$
7 $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$
9 $[9, 3, w^{3} - 4w^{2} - w + 9]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{19}{7}e + \frac{20}{7}$
17 $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $-\frac{1}{2}e^{2} + e + 8$
17 $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{28}e^{3} + \frac{1}{7}e^{2} - \frac{13}{7}e - \frac{18}{7}$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{1}{28}e^{3} + \frac{1}{7}e^{2} - \frac{13}{7}e - \frac{18}{7}$
23 $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ $-\frac{1}{7}e^{3} + \frac{3}{7}e^{2} + \frac{38}{7}e - \frac{40}{7}$
23 $[23, 23, -w^{2} + 2w + 3]$ $-\frac{1}{7}e^{3} + \frac{3}{7}e^{2} + \frac{38}{7}e - \frac{40}{7}$
31 $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{12}{7}e - \frac{22}{7}$
31 $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{12}{7}e - \frac{22}{7}$
41 $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ $-\frac{3}{28}e^{3} + \frac{4}{7}e^{2} + \frac{25}{7}e - \frac{58}{7}$
41 $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ $-\frac{3}{28}e^{3} + \frac{4}{7}e^{2} + \frac{25}{7}e - \frac{58}{7}$
49 $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ $\phantom{-}\frac{3}{14}e^{3} - \frac{9}{14}e^{2} - \frac{36}{7}e + \frac{74}{7}$
71 $[71, 71, w^{2} - 2w - 2]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{5}{7}e^{2} - \frac{12}{7}e + \frac{76}{7}$
71 $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ $\phantom{-}\frac{1}{14}e^{3} - \frac{5}{7}e^{2} - \frac{12}{7}e + \frac{76}{7}$
73 $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$
73 $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$
79 $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ $-\frac{5}{14}e^{3} + \frac{15}{14}e^{2} + \frac{60}{7}e - \frac{58}{7}$
79 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $-\frac{5}{14}e^{3} + \frac{15}{14}e^{2} + \frac{60}{7}e - \frac{58}{7}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).