Properties

Label 6.6.1134389.1-19.1-c
Base field 6.6.1134389.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $19$
Level $[19, 19, w^{3} - w^{2} - 3w + 1]$
Dimension $4$
CM no
Base change no

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Base field 6.6.1134389.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[19, 19, w^{3} - w^{2} - 3w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 8x^{3} + 15x^{2} + 4x - 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{2} - w - 2]$ $\phantom{-}e$
13 $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + \frac{2}{3}e + 1$
17 $[17, 17, -w^{3} + w^{2} + 3w]$ $-\frac{2}{3}e^{3} + 4e^{2} - 3e - \frac{14}{3}$
19 $[19, 19, w^{3} - w^{2} - 3w + 1]$ $-1$
19 $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $-\frac{1}{3}e^{2} + \frac{4}{3}e - \frac{10}{3}$
23 $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{10}{3}e^{2} + \frac{25}{3}e$
31 $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ $-e^{3} + 6e^{2} - 7e$
37 $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $-\frac{1}{3}e^{3} + 2e^{2} - 2e + \frac{5}{3}$
37 $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ $\phantom{-}e^{3} - \frac{16}{3}e^{2} + \frac{4}{3}e + \frac{35}{3}$
47 $[47, 47, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}e^{3} - \frac{23}{3}e^{2} + \frac{29}{3}e + \frac{22}{3}$
64 $[64, 2, -2]$ $-\frac{2}{3}e^{3} + 2e^{2} + 6e - \frac{8}{3}$
67 $[67, 67, 2w - 1]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + \frac{14}{3}e - 7$
79 $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ $\phantom{-}\frac{2}{3}e^{3} - 4e^{2} - 2e + \frac{44}{3}$
79 $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ $\phantom{-}\frac{2}{3}e^{3} - 6e^{2} + 9e + \frac{32}{3}$
97 $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ $-\frac{2}{3}e^{3} + \frac{19}{3}e^{2} - \frac{46}{3}e - \frac{25}{3}$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ $-\frac{5}{3}e^{3} + 12e^{2} - 17e - \frac{14}{3}$
101 $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ $\phantom{-}\frac{5}{3}e^{3} - \frac{22}{3}e^{2} + \frac{1}{3}e + \frac{4}{3}$
101 $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ $\phantom{-}2e^{3} - \frac{32}{3}e^{2} + \frac{11}{3}e + \frac{58}{3}$
103 $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ $\phantom{-}2e^{3} - 11e^{2} + 7e + 11$
107 $[107, 107, w^{2} - 2w - 3]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{19}{3}e^{2} + \frac{34}{3}e + \frac{25}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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