Properties

Label 4.4.17600.1-1.1-a
Base field 4.4.17600.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $8$
CM no
Base change yes

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Base field 4.4.17600.1

Generator \(w\), with minimal polynomial \(x^{4} - 14x^{2} + 44\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $8$
CM: no
Base change: yes
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 36x^{6} + 424x^{4} - 1648x^{2} + 320\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $-\frac{1}{8}e^{6} + 3e^{4} - 18e^{2} + 8$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 11e$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 11e$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 17e$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + 14e^{2}$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + 14e^{2}$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $\phantom{-}\frac{1}{8}e^{5} - 3e^{3} + 17e$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + 14e^{2} + 6$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $\phantom{-}\frac{1}{16}e^{7} - \frac{3}{2}e^{5} + 10e^{3} - 17e$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $\phantom{-}\frac{1}{16}e^{7} - \frac{3}{2}e^{5} + 10e^{3} - 17e$
31 $[31, 31, -w - 1]$ $-\frac{1}{2}e^{3} + 6e$
31 $[31, 31, w - 1]$ $-\frac{1}{2}e^{3} + 6e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $-\frac{1}{16}e^{7} + \frac{11}{8}e^{5} - \frac{13}{2}e^{3} - 7e$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $-\frac{1}{16}e^{7} + \frac{11}{8}e^{5} - \frac{13}{2}e^{3} - 7e$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $-\frac{1}{16}e^{7} + \frac{13}{8}e^{5} - 12e^{3} + 21e$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $-\frac{1}{16}e^{7} + \frac{13}{8}e^{5} - 12e^{3} + 21e$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $-\frac{1}{8}e^{6} + \frac{5}{2}e^{4} - 11e^{2}$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $-\frac{1}{8}e^{6} + \frac{5}{2}e^{4} - 11e^{2}$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $\phantom{-}\frac{1}{4}e^{4} - 2e^{2} - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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