Properties

Label 3.3.81.1-51.1-a
Base field \(\Q(\zeta_{9})^+\)
Weight $[2, 2, 2]$
Level norm $51$
Level $[51, 51, -3w^{2} + 2w + 4]$
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: $[51, 51, -3w^{2} + 2w + 4]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $1$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $-1$
8 $[8, 2, 2]$ $\phantom{-}1$
17 $[17, 17, -2w^{2} + w + 3]$ $\phantom{-}2$
17 $[17, 17, -w^{2} - w + 3]$ $-6$
17 $[17, 17, -w^{2} + 2w + 3]$ $\phantom{-}1$
19 $[19, 19, -2w^{2} + 2w + 5]$ $\phantom{-}4$
19 $[19, 19, -2w^{2} + 3]$ $-4$
19 $[19, 19, -2w + 1]$ $\phantom{-}4$
37 $[37, 37, -w^{2} + 3w + 3]$ $\phantom{-}6$
37 $[37, 37, 2w^{2} + w - 5]$ $-2$
37 $[37, 37, 3w^{2} - 2w - 5]$ $-2$
53 $[53, 53, -w - 4]$ $-2$
53 $[53, 53, -w^{2} + w - 2]$ $-10$
53 $[53, 53, w^{2} - 6]$ $-2$
71 $[71, 71, w^{2} + w - 7]$ $\phantom{-}16$
71 $[71, 71, w^{2} - 2w - 7]$ $-8$
71 $[71, 71, -2w^{2} + w - 1]$ $-8$
73 $[73, 73, 3w^{2} - 3w - 8]$ $-6$
73 $[73, 73, 2w^{2} - 3w - 7]$ $-6$
73 $[73, 73, w^{2} + 2w - 5]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 1]$ $1$
$17$ $[17, 17, -w^{2} + 2w + 3]$ $-1$