Properties

Label 6.6.1202933.1-35.1-a
Base field 6.6.1202933.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $35$
Level $[35, 35, 2w^{5} - 11w^{3} - 4w^{2} + 7w + 1]$
Dimension $1$
CM no
Base change no

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Base field 6.6.1202933.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[35, 35, 2w^{5} - 11w^{3} - 4w^{2} + 7w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $17$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ $-1$
7 $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ $\phantom{-}1$
19 $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ $\phantom{-}0$
23 $[23, 23, -w^{2} + w + 2]$ $\phantom{-}9$
25 $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ $\phantom{-}2$
41 $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ $\phantom{-}5$
47 $[47, 47, w^{3} - w^{2} - 4w]$ $-4$
53 $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ $-12$
59 $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ $-8$
61 $[61, 61, w^{2} - 2w - 2]$ $-2$
64 $[64, 2, -2]$ $-3$
67 $[67, 67, -w^{4} + 6w^{2} + w - 3]$ $-13$
67 $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ $\phantom{-}0$
73 $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ $-8$
73 $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ $-11$
79 $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ $-15$
83 $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ $-4$
89 $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ $-17$
97 $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ $-6$
97 $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ $1$
$7$ $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ $-1$