Properties

Label 4.4.12400.1-1.1-a
Base field 4.4.12400.1
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 4.4.12400.1

Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 31\); 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:

\(x^{6} - 18x^{4} + 94x^{2} - 144\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 19$
5 $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ $-\frac{1}{6}e^{5} + 2e^{3} - \frac{14}{3}e$
9 $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ $-\frac{1}{6}e^{5} + 2e^{3} - \frac{14}{3}e$
19 $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ $-\frac{1}{6}e^{5} + 3e^{3} - \frac{35}{3}e$
19 $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ $-\frac{1}{6}e^{5} + 3e^{3} - \frac{35}{3}e$
29 $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ $\phantom{-}e^{2} - 6$
29 $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ $\phantom{-}e^{2} - 6$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-\frac{1}{3}e^{5} + 4e^{3} - \frac{22}{3}e$
59 $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ $\phantom{-}2e^{2} - 12$
59 $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ $\phantom{-}2e^{2} - 12$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ $-\frac{2}{3}e^{5} + 9e^{3} - \frac{71}{3}e$
61 $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ $-\frac{2}{3}e^{5} + 9e^{3} - \frac{71}{3}e$
71 $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ $\phantom{-}e^{5} - 14e^{3} + 40e$
71 $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ $\phantom{-}e^{5} - 14e^{3} + 40e$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ $\phantom{-}\frac{2}{3}e^{5} - 10e^{3} + \frac{86}{3}e$
79 $[79, 79, -2w^{2} + w + 10]$ $\phantom{-}2e^{4} - 26e^{2} + 64$
79 $[79, 79, 2w^{2} + w - 10]$ $\phantom{-}2e^{4} - 26e^{2} + 64$
79 $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ $\phantom{-}\frac{2}{3}e^{5} - 10e^{3} + \frac{86}{3}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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