Properties

Label 6.6.1259712.1-8.1-a
Base field \(\Q(\zeta_{36})^+\)
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $8$
Level $[8, 2, w^{3} - 3w - 1]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\zeta_{36})^+\)

Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} + 9x^{2} - 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[8, 2, w^{3} - 3w - 1]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}3$
8 $[8, 2, w^{3} - 3w - 1]$ $-1$
37 $[37, 37, w^{4} - 5w^{2} - w + 5]$ $-4$
37 $[37, 37, w^{5} - 5w^{3} - w^{2} + 4w + 1]$ $-4$
37 $[37, 37, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w + 1]$ $-4$
37 $[37, 37, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 5w + 1]$ $-4$
37 $[37, 37, w^{5} - 5w^{3} + w^{2} + 4w - 1]$ $-4$
37 $[37, 37, -w^{4} + 5w^{2} - w - 5]$ $-4$
71 $[71, 71, w^{5} - 5w^{3} - w^{2} + 5w + 4]$ $\phantom{-}12$
71 $[71, 71, w^{5} - 4w^{3} - w^{2} + w + 2]$ $\phantom{-}12$
71 $[71, 71, w^{5} + w^{4} - 5w^{3} - 5w^{2} + 4w + 2]$ $\phantom{-}12$
71 $[71, 71, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 4w - 2]$ $\phantom{-}12$
71 $[71, 71, -w^{5} + 4w^{3} - w^{2} - w + 2]$ $\phantom{-}12$
71 $[71, 71, -w^{5} + 5w^{3} - w^{2} - 5w + 4]$ $\phantom{-}12$
73 $[73, 73, w^{5} - 5w^{3} - w^{2} + 3w + 2]$ $\phantom{-}11$
73 $[73, 73, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 2]$ $\phantom{-}11$
73 $[73, 73, -w^{5} + 4w^{3} - w^{2} - 2w + 2]$ $\phantom{-}11$
73 $[73, 73, w^{5} - 4w^{3} - w^{2} + 2w + 2]$ $\phantom{-}11$
73 $[73, 73, -2w^{5} - w^{4} + 10w^{3} + 4w^{2} - 9w - 2]$ $\phantom{-}11$
73 $[73, 73, w^{5} - 5w^{3} + w^{2} + 3w - 2]$ $\phantom{-}11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$8$ $[8, 2, w^{3} - 3w - 1]$ $1$