Properties

Base field 6.6.434581.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 43
Level $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$
Label 6.6.434581.1-43.1-d
Dimension 2
CM no
Base change no

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Base field 6.6.434581.1

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

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$
Label 6.6.434581.1-43.1-d
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut 2x \) \(\mathstrut -\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 2]$ $-\frac{1}{2}e - 1$
27 $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ $\phantom{-}\frac{5}{2}e + 4$
27 $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ $-\frac{3}{2}e + 5$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ $-\frac{3}{2}e - 4$
29 $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ $\phantom{-}8$
43 $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ $-1$
43 $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ $\phantom{-}3e + 2$
49 $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ $-\frac{1}{2}e + 2$
64 $[64, 2, -2]$ $-e - 9$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ $\phantom{-}\frac{7}{2}e + 1$
71 $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ $\phantom{-}5e + 2$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $\phantom{-}2e$
71 $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ $-4e - 4$
83 $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ $\phantom{-}\frac{3}{2}e - 3$
83 $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ $-\frac{5}{2}e + 9$
83 $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ $-6e - 8$
83 $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ $-6e - 8$
97 $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ $-\frac{5}{2}e - 10$
97 $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ $\phantom{-}\frac{1}{2}e + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
43 $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ $1$