Properties

Label 4.4.6809.1-16.1-d
Base field 4.4.6809.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $3$
CM no
Base change no

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Base field 4.4.6809.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - x^{2} - 14x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}e$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 5w + 1]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 5$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 5$
23 $[23, 23, -w^{2} + 2]$ $-e^{2} - e + 10$
29 $[29, 29, -w^{2} - w + 3]$ $\phantom{-}e^{2} + e - 12$
31 $[31, 31, -w^{3} + 6w + 2]$ $\phantom{-}e^{2} - 4$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e + 1$
47 $[47, 47, 2w^{3} - 9w]$ $-e - 2$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $-e - 2$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $-2$
59 $[59, 59, w^{2} - w - 5]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 3$
59 $[59, 59, 3w^{3} - 15w - 5]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 3$
71 $[71, 71, w^{3} - 3w - 3]$ $\phantom{-}e^{2} - e - 14$
81 $[81, 3, -3]$ $\phantom{-}4e + 2$
83 $[83, 83, -2w^{3} + 8w + 3]$ $-\frac{1}{2}e^{2} + \frac{5}{2}e + 3$
89 $[89, 89, -2w^{3} + 11w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 3$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $-e - 4$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $-2e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w + 1]$ $-1$
$8$ $[8, 2, w^{3} - w^{2} - 4w + 3]$ $-1$