Properties

Label 4.4.10512.1-16.1-b
Base field 4.4.10512.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $4$
CM no
Base change yes

Related objects

Downloads

Learn more

Base field 4.4.10512.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - 6x + 1\); narrow class number \(4\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 48x^{2} + 384\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}0$
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $-\frac{1}{4}e^{2} + 8$
11 $[11, 11, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $-\frac{1}{4}e^{2} + 4$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{1}{4}e^{2} + 4$
23 $[23, 23, w^{2} - 2w - 2]$ $\phantom{-}\frac{1}{8}e^{3} - 4e$
23 $[23, 23, w^{3} - w^{2} - 6w - 3]$ $\phantom{-}0$
23 $[23, 23, -w^{2} + 2w + 5]$ $\phantom{-}\frac{1}{8}e^{3} - 4e$
23 $[23, 23, -w + 2]$ $\phantom{-}0$
37 $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ $\phantom{-}2$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ $-\frac{1}{4}e^{2} + 4$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ $-\frac{1}{4}e^{2} + 4$
37 $[37, 37, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}2$
47 $[47, 47, w^{2} - 2w - 1]$ $\phantom{-}\frac{1}{8}e^{3} - 4e$
47 $[47, 47, w^{2} - 2w - 6]$ $\phantom{-}\frac{1}{8}e^{3} - 4e$
59 $[59, 59, 2w - 1]$ $-\frac{1}{8}e^{3} + 3e$
59 $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ $-\frac{1}{8}e^{3} + 3e$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-e^{2} + 26$
83 $[83, 83, -w^{3} + w^{2} + 4w + 3]$ $\phantom{-}\frac{1}{8}e^{3} - 3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w^{3} - w^{2} - 5w - 2]$ $1$