Properties

Label 4.4.13625.1-1.1-a
Base field 4.4.13625.1
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 4.4.13625.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); 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:

\(x^{6} - 15x^{4} + 58x^{2} - 20\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ $\phantom{-}e$
5 $[5, 5, w - 3]$ $-e^{3} + 7e$
11 $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 4$
11 $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 4$
19 $[19, 19, -w^{2} + 2w + 4]$ $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 13e$
19 $[19, 19, -w^{2} + 5]$ $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 13e$
31 $[31, 31, w]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} - 1$
31 $[31, 31, w + 3]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} - 1$
31 $[31, 31, -w + 4]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} - 1$
31 $[31, 31, w - 1]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} - 1$
41 $[41, 41, -w^{2} + 2]$ $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 4$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 4$
59 $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 4e$
59 $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 4e$
79 $[79, 79, -w^{2} + 8]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$
79 $[79, 79, w^{2} - 2w - 7]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$
81 $[81, 3, -3]$ $-\frac{3}{2}e^{4} + \frac{19}{2}e^{2} + 14$
101 $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} - 11$
101 $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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