Properties

Label 4.4.16225.1-1.1-a
Base field 4.4.16225.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $6$
CM no
Base change yes

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Base field 4.4.16225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 6x + 36\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $6$
CM: no
Base change: yes
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 11x^{4} + 21x^{2} - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ $\phantom{-}\frac{1}{2}e^{4} - 5e^{2} + \frac{11}{2}$
9 $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ $\phantom{-}\frac{1}{2}e^{4} - 5e^{2} + \frac{11}{2}$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ $-e^{5} + 10e^{3} - 13e$
19 $[19, 19, w + 1]$ $\phantom{-}e^{5} - 11e^{3} + 20e$
19 $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ $\phantom{-}e^{5} - 11e^{3} + 20e$
25 $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $\phantom{-}e^{2} + 1$
29 $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ $-\frac{1}{2}e^{5} + 6e^{3} - \frac{29}{2}e$
29 $[29, 29, w - 1]$ $-\frac{1}{2}e^{5} + 6e^{3} - \frac{29}{2}e$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ $-e^{3} + 7e$
31 $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ $-e^{3} + 7e$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ $-\frac{3}{2}e^{5} + 16e^{3} - \frac{55}{2}e$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ $-\frac{3}{2}e^{5} + 16e^{3} - \frac{55}{2}e$
59 $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-e^{4} + 8e^{2} - 3$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ $-e^{4} + 8e^{2} - 3$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ $-e^{4} + 8e^{2} - 3$
79 $[79, 79, w^{2} - 11]$ $-e^{4} + 9e^{2} - 8$
79 $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ $-e^{4} + 9e^{2} - 8$
89 $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ $\phantom{-}\frac{5}{2}e^{5} - 27e^{3} + \frac{91}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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