Properties

Label 6.6.1416125.1-19.2-a
Base field 6.6.1416125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$
Dimension $4$
CM no
Base change no

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Base field 6.6.1416125.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 6x^{3} + 6x^{2} - 8x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ $\phantom{-}e$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{1}{2}e^{2} + 2e - 1$
19 $[19, 19, -w^{3} + 4w]$ $\phantom{-}e^{3} + 4e^{2} - e - 6$
19 $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ $\phantom{-}1$
19 $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ $\phantom{-}e^{3} + \frac{9}{2}e^{2} - 4$
25 $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ $-\frac{1}{2}e^{3} - 4e^{2} - 6e + 4$
29 $[29, 29, -w^{3} + 4w + 1]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 2e + 2$
41 $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $-\frac{3}{2}e^{3} - \frac{17}{2}e^{2} - 7e + 5$
49 $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ $-\frac{3}{2}e^{3} - \frac{15}{2}e^{2} - 4e + 3$
59 $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - 2e - 9$
59 $[59, 59, -w^{3} + w^{2} + 2w - 3]$ $-\frac{1}{2}e^{3} - \frac{7}{2}e^{2} - 3e + 1$
61 $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ $-e^{3} - 5e^{2} + 4$
64 $[64, 2, -2]$ $\phantom{-}2e^{3} + 10e^{2} + 7e - 11$
71 $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2}$
71 $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ $-e^{3} - \frac{5}{2}e^{2} + 2e - 4$
79 $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ $-e^{3} - \frac{15}{2}e^{2} - 7e + 14$
79 $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ $\phantom{-}e^{3} + \frac{9}{2}e^{2} + 4e + 7$
89 $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ $\phantom{-}e^{3} + 6e^{2} + 6e - 6$
109 $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ $\phantom{-}\frac{5}{2}e^{2} + 8e - 5$
109 $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ $\phantom{-}\frac{3}{2}e^{3} + 8e^{2} + 5e - 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ $-1$