Properties

Label 3.3.785.1-8.1-a
Base field 3.3.785.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.785.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 2, 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}0$
5 $[5, 5, w]$ $\phantom{-}e$
5 $[5, 5, -w + 3]$ $-e - 1$
8 $[8, 2, 2]$ $\phantom{-}1$
9 $[9, 3, w^{2} + w - 4]$ $-e - 1$
13 $[13, 13, w + 3]$ $\phantom{-}e$
17 $[17, 17, -w^{2} + w + 3]$ $-e - 5$
23 $[23, 23, w^{2} - 2]$ $\phantom{-}0$
23 $[23, 23, w^{2} - 3]$ $\phantom{-}4$
23 $[23, 23, -w^{2} + 8]$ $\phantom{-}4$
29 $[29, 29, w - 4]$ $\phantom{-}e + 4$
37 $[37, 37, w^{2} + w - 8]$ $\phantom{-}e + 8$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}e + 4$
47 $[47, 47, 2w^{2} + w - 8]$ $\phantom{-}4$
59 $[59, 59, -2w^{2} - 3w + 6]$ $-4e - 4$
61 $[61, 61, -2w - 1]$ $-e + 7$
67 $[67, 67, -2w - 3]$ $\phantom{-}8$
79 $[79, 79, 2w^{2} - 9]$ $\phantom{-}8$
109 $[109, 109, w^{2} + 2w - 6]$ $-2$
109 $[109, 109, 2w^{2} + w - 14]$ $\phantom{-}3e + 7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$8$ $[8, 2, 2]$ $-1$