Properties

Label 6.6.1081856.1-49.2-f
Base field 6.6.1081856.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $49$
Level $[49, 49, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - 2w + 2]$
Dimension $2$
CM no
Base change no

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Base field 6.6.1081856.1

Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 7x^{2} + 2x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[49, 49, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - 2w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ $\phantom{-}0$
8 $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ $\phantom{-}e$
17 $[17, 17, -w^{2} + w + 2]$ $\phantom{-}\frac{1}{4}e$
23 $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ $\phantom{-}\frac{3}{2}e$
25 $[25, 5, -w^{3} + w^{2} + 4w]$ $\phantom{-}\frac{3}{4}e$
31 $[31, 31, -w^{3} + 4w + 1]$ $\phantom{-}4$
31 $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ $-\frac{3}{2}e$
41 $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ $-\frac{7}{4}e$
47 $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ $-\frac{1}{2}e$
49 $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ $-\frac{5}{4}e$
71 $[71, 71, -w^{4} + 5w^{2} + w - 3]$ $\phantom{-}e$
71 $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ $\phantom{-}16$
73 $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ $\phantom{-}4$
73 $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ $-10$
79 $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ $-2e$
89 $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ $\phantom{-}6$
97 $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ $\phantom{-}0$
103 $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ $\phantom{-}3e$
103 $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ $-\frac{1}{2}e$
103 $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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