Properties

Base field \(\Q(\zeta_{9})^+\)
Weight [2, 2, 2]
Level norm 27
Level $[27, 3, 3]$
Label 3.3.81.1-27.1-a
Dimension 1
CM yes
Base change yes

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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 $[27, 3, 3]$
Label 3.3.81.1-27.1-a
Dimension 1
Is CM yes
Is base change yes
Parent newspace dimension 1

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}0$
8 $[8, 2, 2]$ $\phantom{-}0$
17 $[17, 17, -2w^{2} + w + 3]$ $\phantom{-}0$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}0$
17 $[17, 17, -w^{2} + 2w + 3]$ $\phantom{-}0$
19 $[19, 19, -2w^{2} + 2w + 5]$ $-7$
19 $[19, 19, -2w^{2} + 3]$ $-7$
19 $[19, 19, -2w + 1]$ $-7$
37 $[37, 37, -w^{2} + 3w + 3]$ $\phantom{-}11$
37 $[37, 37, 2w^{2} + w - 5]$ $\phantom{-}11$
37 $[37, 37, 3w^{2} - 2w - 5]$ $\phantom{-}11$
53 $[53, 53, -w - 4]$ $\phantom{-}0$
53 $[53, 53, -w^{2} + w - 2]$ $\phantom{-}0$
53 $[53, 53, w^{2} - 6]$ $\phantom{-}0$
71 $[71, 71, w^{2} + w - 7]$ $\phantom{-}0$
71 $[71, 71, w^{2} - 2w - 7]$ $\phantom{-}0$
71 $[71, 71, -2w^{2} + w - 1]$ $\phantom{-}0$
73 $[73, 73, 3w^{2} - 3w - 8]$ $-7$
73 $[73, 73, 2w^{2} - 3w - 7]$ $-7$
73 $[73, 73, w^{2} + 2w - 5]$ $-7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $-1$