Properties

Label 4.4.11197.1-16.1-b
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $6$
CM no
Base change no

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Base field 4.4.11197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 12x^{4} + 33x^{2} - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}\frac{1}{4}e^{5} - 3e^{3} + \frac{33}{4}e$
11 $[11, 11, -w - 2]$ $\phantom{-}3$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1}{2}e^{5} + 5e^{3} - \frac{15}{2}e$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{4}e^{5} - 3e^{3} + \frac{25}{4}e$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{17}{2}e$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{4}e^{5} - 3e^{3} + \frac{41}{4}e$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}2e^{2} - 8$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $-\frac{3}{4}e^{5} + 7e^{3} - \frac{39}{4}e$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}\frac{1}{2}e^{5} - 6e^{3} + \frac{29}{2}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}\frac{1}{2}e^{5} - 6e^{3} + \frac{29}{2}e$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $-e^{4} + 10e^{2} - 15$
47 $[47, 47, w^{2} - 3w - 2]$ $-e^{5} + 10e^{3} - 15e$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e^{4} - 10e^{2} + 7$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}e^{4} - 10e^{2} + 13$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $\phantom{-}3e^{2} - 14$
83 $[83, 83, -2w + 3]$ $\phantom{-}2e^{2} - 8$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $-\frac{1}{2}e^{5} + 6e^{3} - \frac{35}{2}e$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $\phantom{-}2e^{4} - 19e^{2} + 30$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$