Properties

Label 3.3.81.1-111.2-a
Base field \(\Q(\zeta_{9})^+\)
Weight $[2, 2, 2]$
Level norm $111$
Level $[111,111,3w^{2} + w - 10]$
Dimension $1$
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: $[111,111,3w^{2} + w - 10]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $-1$
8 $[8, 2, 2]$ $\phantom{-}5$
17 $[17, 17, -2w^{2} + w + 3]$ $\phantom{-}2$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}6$
17 $[17, 17, -w^{2} + 2w + 3]$ $-2$
19 $[19, 19, -2w^{2} + 2w + 5]$ $-8$
19 $[19, 19, -2w^{2} + 3]$ $\phantom{-}0$
19 $[19, 19, -2w + 1]$ $-4$
37 $[37, 37, -w^{2} + 3w + 3]$ $\phantom{-}2$
37 $[37, 37, 2w^{2} + w - 5]$ $-10$
37 $[37, 37, 3w^{2} - 2w - 5]$ $\phantom{-}1$
53 $[53, 53, -w - 4]$ $\phantom{-}6$
53 $[53, 53, -w^{2} + w - 2]$ $-14$
53 $[53, 53, w^{2} - 6]$ $\phantom{-}6$
71 $[71, 71, w^{2} + w - 7]$ $-8$
71 $[71, 71, w^{2} - 2w - 7]$ $\phantom{-}0$
71 $[71, 71, -2w^{2} + w - 1]$ $\phantom{-}8$
73 $[73, 73, 3w^{2} - 3w - 8]$ $-14$
73 $[73, 73, 2w^{2} - 3w - 7]$ $-2$
73 $[73, 73, w^{2} + 2w - 5]$ $\phantom{-}10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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