Properties

Label 6.6.1229312.1-8.1-c
Base field 6.6.1229312.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $8$
Level $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$
Dimension $1$
CM no
Base change yes

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Base field 6.6.1229312.1

Generator \(w\), with minimal polynomial \(x^{6} - 10x^{4} + 24x^{2} - 8\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ $-1$
7 $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ $-1$
8 $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ $-1$
41 $[41, 41, -\frac{1}{4}w^{4} - \frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 1]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{2}w^{2} - w + 2]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + 2w^{2} - 5w - 2]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{4}w^{5} - \frac{1}{4}w^{4} - \frac{5}{2}w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{2}w^{2} - w - 2]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 1]$ $\phantom{-}0$
71 $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + w^{2} - 5w + 1]$ $\phantom{-}12$
71 $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + \frac{3}{2}w^{2} - 6w - 2]$ $\phantom{-}12$
71 $[71, 71, \frac{1}{4}w^{4} - \frac{1}{2}w^{3} - \frac{5}{2}w^{2} + 3w + 4]$ $-9$
71 $[71, 71, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - 3w + 4]$ $\phantom{-}12$
71 $[71, 71, \frac{1}{2}w^{4} - \frac{7}{2}w^{2} + w + 3]$ $-9$
71 $[71, 71, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + \frac{5}{2}w^{3} - w^{2} - 5w - 1]$ $-9$
97 $[97, 97, \frac{1}{4}w^{5} - \frac{5}{2}w^{3} - \frac{1}{2}w^{2} + 5w]$ $\phantom{-}14$
97 $[97, 97, -\frac{1}{4}w^{4} + \frac{3}{2}w^{2} + w + 1]$ $-7$
97 $[97, 97, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + 2w^{2} - 3w - 4]$ $\phantom{-}14$
97 $[97, 97, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - 2w^{2} - 3w + 4]$ $-7$
97 $[97, 97, \frac{1}{4}w^{4} - \frac{3}{2}w^{2} + w - 1]$ $\phantom{-}14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$8$ $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ $1$