Properties

Label 3.3.81.1-111.3-b
Base field \(\Q(\zeta_{9})^+\)
Weight $[2, 2, 2]$
Level norm $111$
Level $[111,111,w^{2} - 4w - 6]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\zeta_{9})^+\)

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

Form

Weight: $[2, 2, 2]$
Level: $[111,111,w^{2} - 4w - 6]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}1$
8 $[8, 2, 2]$ $\phantom{-}e$
17 $[17, 17, -2w^{2} + w + 3]$ $-2e - 2$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}2e$
17 $[17, 17, -w^{2} + 2w + 3]$ $-2e - 2$
19 $[19, 19, -2w^{2} + 2w + 5]$ $\phantom{-}2e + 2$
19 $[19, 19, -2w^{2} + 3]$ $-2e$
19 $[19, 19, -2w + 1]$ $-2e$
37 $[37, 37, -w^{2} + 3w + 3]$ $\phantom{-}4e + 2$
37 $[37, 37, 2w^{2} + w - 5]$ $-1$
37 $[37, 37, 3w^{2} - 2w - 5]$ $\phantom{-}0$
53 $[53, 53, -w - 4]$ $-2e - 4$
53 $[53, 53, -w^{2} + w - 2]$ $-2e - 4$
53 $[53, 53, w^{2} - 6]$ $\phantom{-}2e - 2$
71 $[71, 71, w^{2} + w - 7]$ $-4$
71 $[71, 71, w^{2} - 2w - 7]$ $-4$
71 $[71, 71, -2w^{2} + w - 1]$ $-4$
73 $[73, 73, 3w^{2} - 3w - 8]$ $\phantom{-}4e$
73 $[73, 73, 2w^{2} - 3w - 7]$ $-2$
73 $[73, 73, w^{2} + 2w - 5]$ $-2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3,3,w^{2} - 1]$ $-1$
$37$ $[37,37,-2w^{2} - w + 5]$ $1$