Properties

Label 3.3.1016.1-16.2-f
Base field 3.3.1016.1
Weight $[2, 2, 2]$
Level norm $16$
Level $[16, 4, -w^{2} + 6]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.1016.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[16, 4, -w^{2} + 6]$
Dimension: $2$
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:

\(x^{2} - x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, w - 3]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 5]$ $\phantom{-}e - 1$
9 $[9, 3, w^{2} + w - 1]$ $\phantom{-}0$
13 $[13, 13, 2w^{2} - 2w - 11]$ $\phantom{-}2e - 2$
29 $[29, 29, -w^{2} - 3w - 1]$ $\phantom{-}3e - 3$
29 $[29, 29, -w^{2} + w + 3]$ $-2e + 6$
29 $[29, 29, 2w - 5]$ $-e + 7$
31 $[31, 31, -w^{2} + w + 1]$ $-3e + 3$
37 $[37, 37, -2w - 1]$ $-e - 7$
43 $[43, 43, -2w - 3]$ $-2e - 6$
47 $[47, 47, 2w - 3]$ $\phantom{-}2e - 2$
59 $[59, 59, 4w^{2} + 8w - 1]$ $-2e + 6$
61 $[61, 61, -w^{2} - w - 1]$ $\phantom{-}5e - 7$
67 $[67, 67, w^{2} + w - 5]$ $-e + 1$
71 $[71, 71, w^{2} - w - 9]$ $\phantom{-}e + 11$
73 $[73, 73, -2w^{2} + 2w + 9]$ $-2e + 10$
73 $[73, 73, 6w^{2} + 10w - 7]$ $\phantom{-}6$
73 $[73, 73, 3w^{2} - 3w - 17]$ $\phantom{-}e - 1$
79 $[79, 79, -2w^{2} + 2w + 15]$ $-e + 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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