Properties

Label 4.4.11344.1-16.1-f
Base field 4.4.11344.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.11344.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 11x^{2} + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
11 $[11, 11, w + 2]$ $\phantom{-}e^{2} - 4$
27 $[27, 3, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}e$
29 $[29, 29, -w^{2} + 3w + 1]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
31 $[31, 31, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}2e$
31 $[31, 31, -w^{2} + 2w + 4]$ $-2e$
47 $[47, 47, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}0$
49 $[49, 7, 2w^{3} - 2w^{2} - 8w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e$
49 $[49, 7, w^{3} - w^{2} - 3w - 2]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e$
53 $[53, 53, w^{3} - 3w^{2} - w + 2]$ $-2e^{2} + 14$
53 $[53, 53, w^{3} - 5w - 5]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
61 $[61, 61, 2w - 1]$ $-\frac{1}{2}e^{3} + \frac{15}{2}e$
61 $[61, 61, -w^{3} + 4w^{2} - 4]$ $-2e^{2} + 6$
67 $[67, 67, 3w^{3} - 3w^{2} - 13w - 4]$ $\phantom{-}e^{3} - 9e$
73 $[73, 73, -w^{3} + 4w^{2} - 10]$ $-\frac{1}{2}e^{3} + \frac{17}{2}e$
73 $[73, 73, w^{2} - w + 1]$ $\phantom{-}3e^{2} - 14$
83 $[83, 83, -4w^{3} + 5w^{2} + 17w + 1]$ $\phantom{-}3e^{2} - 12$
83 $[83, 83, 3w^{3} - 3w^{2} - 14w - 5]$ $-e^{2} + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w - 1]$ $1$