Properties

Label 6.6.980125.1-41.3-j
Base field 6.6.980125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$
Dimension $2$
CM no
Base change no

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Base field 6.6.980125.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 5x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 17\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}3$
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $-e + 3$
11 $[11, 11, -w^{5} + 6w^{3} - w^{2} - 7w + 1]$ $\phantom{-}e$
19 $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ $-\frac{1}{3}e - \frac{11}{3}$
29 $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ $\phantom{-}\frac{4}{3}e + \frac{5}{3}$
31 $[31, 31, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ $\phantom{-}e - 1$
41 $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ $\phantom{-}\frac{2}{3}e - \frac{26}{3}$
41 $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 6w - 3]$ $\phantom{-}e + 3$
41 $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $-1$
59 $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ $-e + 9$
59 $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ $-\frac{1}{3}e - \frac{38}{3}$
59 $[59, 59, -w^{5} + 4w^{3} - w^{2} - w + 1]$ $\phantom{-}\frac{5}{3}e + \frac{10}{3}$
61 $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ $-1$
64 $[64, 2, -2]$ $-\frac{5}{3}e - \frac{16}{3}$
71 $[71, 71, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 9w + 3]$ $-\frac{5}{3}e + \frac{8}{3}$
81 $[81, 3, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{3}e + \frac{23}{3}$
89 $[89, 89, -w^{5} + 6w^{3} - 7w]$ $\phantom{-}2$
89 $[89, 89, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 6w + 2]$ $-2e + 2$
101 $[101, 101, w^{5} - 4w^{3} + 2w^{2} + w - 3]$ $\phantom{-}\frac{10}{3}e - \frac{7}{3}$
101 $[101, 101, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 3w + 4]$ $-\frac{2}{3}e + \frac{5}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $1$