Properties

Label 3.3.785.1-23.1-b
Base field 3.3.785.1
Weight $[2, 2, 2]$
Level norm $23$
Level $[23, 23, w^{2} - 2]$
Dimension $6$
CM no
Base change no

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Base field 3.3.785.1

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

Form

Weight: $[2, 2, 2]$
Level: $[23, 23, w^{2} - 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $23$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - x^{5} - 10x^{4} + 18x^{3} + x^{2} - 11x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $-\frac{18}{13}e^{5} - \frac{4}{13}e^{4} + \frac{165}{13}e^{3} - \frac{131}{13}e^{2} - \frac{103}{13}e + \frac{49}{13}$
5 $[5, 5, -w + 3]$ $\phantom{-}\frac{16}{13}e^{5} + \frac{5}{13}e^{4} - \frac{151}{13}e^{3} + \frac{89}{13}e^{2} + \frac{106}{13}e - \frac{19}{13}$
8 $[8, 2, 2]$ $\phantom{-}\frac{5}{13}e^{5} + \frac{4}{13}e^{4} - \frac{35}{13}e^{3} + \frac{27}{13}e^{2} - \frac{14}{13}e + \frac{3}{13}$
9 $[9, 3, w^{2} + w - 4]$ $\phantom{-}\frac{8}{13}e^{5} + \frac{9}{13}e^{4} - \frac{69}{13}e^{3} - \frac{1}{13}e^{2} + \frac{66}{13}e + \frac{10}{13}$
13 $[13, 13, w + 3]$ $\phantom{-}\frac{11}{13}e^{5} + \frac{1}{13}e^{4} - \frac{116}{13}e^{3} + \frac{62}{13}e^{2} + \frac{133}{13}e - \frac{22}{13}$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}\frac{5}{13}e^{5} - \frac{9}{13}e^{4} - \frac{48}{13}e^{3} + \frac{131}{13}e^{2} - \frac{27}{13}e - \frac{75}{13}$
23 $[23, 23, w^{2} - 2]$ $-1$
23 $[23, 23, w^{2} - 3]$ $-\frac{2}{13}e^{5} + \frac{1}{13}e^{4} + \frac{27}{13}e^{3} - \frac{3}{13}e^{2} - \frac{49}{13}e - \frac{61}{13}$
23 $[23, 23, -w^{2} + 8]$ $-2e^{5} - 2e^{4} + 18e^{3} - 20e - 3$
29 $[29, 29, w - 4]$ $-\frac{19}{13}e^{5} - \frac{10}{13}e^{4} + \frac{172}{13}e^{3} - \frac{87}{13}e^{2} - \frac{108}{13}e - \frac{1}{13}$
37 $[37, 37, w^{2} + w - 8]$ $-\frac{24}{13}e^{5} - \frac{1}{13}e^{4} + \frac{233}{13}e^{3} - \frac{205}{13}e^{2} - \frac{185}{13}e + \frac{87}{13}$
41 $[41, 41, w^{2} + 2w - 4]$ $-3e^{5} - 3e^{4} + 25e^{3} - 3e^{2} - 19e - 4$
47 $[47, 47, 2w^{2} + w - 8]$ $\phantom{-}\frac{25}{13}e^{5} - \frac{6}{13}e^{4} - \frac{227}{13}e^{3} + \frac{291}{13}e^{2} + \frac{8}{13}e - \frac{180}{13}$
59 $[59, 59, -2w^{2} - 3w + 6]$ $-\frac{21}{13}e^{5} - \frac{9}{13}e^{4} + \frac{173}{13}e^{3} - \frac{142}{13}e^{2} - \frac{14}{13}e + \frac{16}{13}$
61 $[61, 61, -2w - 1]$ $-\frac{5}{13}e^{5} + \frac{9}{13}e^{4} + \frac{61}{13}e^{3} - \frac{92}{13}e^{2} - \frac{12}{13}e - \frac{55}{13}$
67 $[67, 67, -2w - 3]$ $-\frac{53}{13}e^{5} + \frac{7}{13}e^{4} + \frac{501}{13}e^{3} - \frac{528}{13}e^{2} - \frac{200}{13}e + \frac{119}{13}$
79 $[79, 79, 2w^{2} - 9]$ $\phantom{-}\frac{50}{13}e^{5} + \frac{27}{13}e^{4} - \frac{480}{13}e^{3} + \frac{179}{13}e^{2} + \frac{497}{13}e - \frac{61}{13}$
109 $[109, 109, w^{2} + 2w - 6]$ $-\frac{28}{13}e^{5} - \frac{25}{13}e^{4} + \frac{261}{13}e^{3} - \frac{29}{13}e^{2} - \frac{309}{13}e + \frac{30}{13}$
109 $[109, 109, 2w^{2} + w - 14]$ $-\frac{74}{13}e^{5} - \frac{2}{13}e^{4} + \frac{713}{13}e^{3} - \frac{618}{13}e^{2} - \frac{487}{13}e + \frac{265}{13}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, w^{2} - 2]$ $1$