Properties

Label 6.6.1995125.1-19.1-b
Base field 6.6.1995125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, w^{3} - w^{2} - 4w]$
Dimension $3$
CM no
Base change no

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Base field 6.6.1995125.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[19, 19, w^{3} - w^{2} - 4w]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + x^{2} - 23x - 25\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ $\phantom{-}\frac{2}{17}e^{2} - \frac{14}{17}e - \frac{70}{17}$
11 $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ $\phantom{-}\frac{3}{17}e^{2} - \frac{4}{17}e - \frac{105}{17}$
11 $[11, 11, w - 1]$ $\phantom{-}e$
19 $[19, 19, w^{3} - w^{2} - 4w]$ $\phantom{-}1$
19 $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ $-\frac{7}{17}e^{2} - \frac{2}{17}e + \frac{75}{17}$
29 $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ $\phantom{-}\frac{5}{17}e^{2} - \frac{1}{17}e - \frac{39}{17}$
29 $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ $-\frac{7}{17}e^{2} - \frac{2}{17}e + \frac{41}{17}$
29 $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ $-2$
29 $[29, 29, -w^{4} + 4w^{3} - 9w]$ $-\frac{5}{17}e^{2} + \frac{18}{17}e + \frac{107}{17}$
31 $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ $\phantom{-}\frac{3}{17}e^{2} - \frac{4}{17}e - \frac{20}{17}$
41 $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ $-\frac{5}{17}e^{2} - \frac{16}{17}e + \frac{22}{17}$
59 $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ $\phantom{-}\frac{3}{17}e^{2} + \frac{13}{17}e - \frac{71}{17}$
61 $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ $\phantom{-}\frac{1}{17}e^{2} + \frac{44}{17}e - \frac{69}{17}$
61 $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ $\phantom{-}\frac{1}{17}e^{2} + \frac{10}{17}e - \frac{103}{17}$
61 $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ $-\frac{6}{17}e^{2} - \frac{43}{17}e + \frac{142}{17}$
61 $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ $\phantom{-}\frac{2}{17}e^{2} - \frac{14}{17}e + \frac{66}{17}$
64 $[64, 2, -2]$ $-\frac{5}{17}e^{2} - \frac{33}{17}e + \frac{39}{17}$
79 $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ $-\frac{8}{17}e^{2} - \frac{12}{17}e + \frac{212}{17}$
89 $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ $-\frac{9}{17}e^{2} + \frac{12}{17}e + \frac{230}{17}$
101 $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ $-\frac{14}{17}e^{2} + \frac{47}{17}e + \frac{286}{17}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, w^{3} - w^{2} - 4w]$ $-1$