Properties

Label 4.4.13888.1-7.3-c
Base field 4.4.13888.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7,7,w - 1]$
Dimension $3$
CM no
Base change no

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Base field 4.4.13888.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 6x + 9\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[7,7,w - 1]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 2x^{2} - 6x - 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $-e^{2} + e + 8$
7 $[7, 7, w - 2]$ $-e^{2} + 7$
7 $[7, 7, w - 1]$ $-1$
9 $[9, 3, w]$ $\phantom{-}2e^{2} + e - 9$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $-e^{2} - e + 6$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $\phantom{-}2e^{2} - e - 11$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $-e^{2} + e + 6$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $-2e^{2} - e + 5$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $\phantom{-}3e^{2} + e - 12$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $-2e^{2} + 4$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $-2e^{2} + 12$
47 $[47, 47, w^{2} - w - 4]$ $\phantom{-}4e^{2} - 20$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $-3e^{2} - 5e + 14$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $\phantom{-}6$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-2e^{2} - 3e + 5$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $-3e - 1$
79 $[79, 79, w^{2} - 5]$ $-e^{2} - 2e - 3$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $\phantom{-}e^{2} - 3e - 4$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $\phantom{-}4e^{2} - 2e - 26$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7,7,w - 1]$ $1$