Properties

Label 6.6.1387029.1-25.1-d
Base field 6.6.1387029.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$
Dimension $2$
CM no
Base change yes

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Base field 6.6.1387029.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - x^{2} - 4x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$
Dimension: $2$
CM: no
Base change: yes
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ $\phantom{-}2e$
25 $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ $-1$
37 $[37, 37, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}3e$
37 $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}3e$
49 $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 3]$ $\phantom{-}6e$
49 $[49, 7, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 4]$ $\phantom{-}6e$
53 $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ $\phantom{-}7e$
53 $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $\phantom{-}7e$
61 $[61, 61, -3w^{5} + 6w^{4} + 12w^{3} - 16w^{2} - 12w + 5]$ $\phantom{-}10$
61 $[61, 61, 2w^{5} - 5w^{4} - 7w^{3} + 16w^{2} + 7w - 7]$ $-4e$
61 $[61, 61, -2w^{5} + 5w^{4} + 7w^{3} - 15w^{2} - 8w + 6]$ $-4e$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}10$
64 $[64, 2, -2]$ $\phantom{-}13$
67 $[67, 67, w^{5} - 3w^{4} - 3w^{3} + 10w^{2} + 2w - 3]$ $-9e$
67 $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 5]$ $-9e$
71 $[71, 71, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 2w - 4]$ $-6$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $-6$
81 $[81, 3, -w^{4} + 2w^{3} + 2w^{2} - 3w + 2]$ $\phantom{-}17$
101 $[101, 101, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 3]$ $-7e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ $1$