Properties

Label 4.4.17609.1-16.2-e
Base field 4.4.17609.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 16, w + 1]$
Dimension $4$
CM no
Base change no

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Base field 4.4.17609.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 16, w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + x^{3} - 20x^{2} - 8x + 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $-\frac{1}{8}e^{3} - \frac{1}{8}e^{2} + \frac{3}{2}e + 2$
7 $[7, 7, -w^{3} + 6w - 2]$ $\phantom{-}e$
8 $[8, 2, w^{3} - 7w + 3]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 5$
11 $[11, 11, -w^{3} + 6w - 4]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - 3e$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $-\frac{1}{8}e^{3} - \frac{1}{8}e^{2} + \frac{5}{2}e - 2$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{3}{8}e^{2} - 2e + 6$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $-4$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{3}{8}e^{2} - e + 6$
41 $[41, 41, w^{2} + 2w - 4]$ $-\frac{1}{8}e^{3} + \frac{3}{8}e^{2} + e - 2$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 6e + 4$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - 4e - 4$
59 $[59, 59, -2w^{3} + 13w - 6]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - 4e + 4$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $-e^{2} - e + 12$
59 $[59, 59, w^{2} + w - 1]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - 5e - 4$
59 $[59, 59, w^{2} + 2w - 6]$ $-\frac{1}{4}e^{3} - \frac{5}{4}e^{2} + 3e + 12$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $-\frac{3}{8}e^{3} - \frac{7}{8}e^{2} + 4e + 10$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $-e^{2} - e + 8$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{5}{4}e^{2} - 3e - 10$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{9}{8}e^{2} - \frac{3}{2}e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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