Properties

Label 3.3.785.1-23.2-c
Base field 3.3.785.1
Weight $[2, 2, 2]$
Level norm $23$
Level $[23, 23, w^{2} - 3]$
Dimension $5$
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: $[23, 23, w^{2} - 3]$
Dimension: $5$
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:

\(x^{5} - 12x^{3} + 4x^{2} + 20x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}0$
5 $[5, 5, -w + 3]$ $-\frac{1}{6}e^{4} - \frac{1}{6}e^{3} + \frac{4}{3}e^{2} + \frac{2}{3}e - \frac{2}{3}$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{1}{3}e^{3} - \frac{11}{3}e^{2} - \frac{7}{3}e + \frac{13}{3}$
9 $[9, 3, w^{2} + w - 4]$ $-\frac{1}{3}e^{4} - \frac{1}{3}e^{3} + \frac{11}{3}e^{2} + \frac{4}{3}e - \frac{10}{3}$
13 $[13, 13, w + 3]$ $\phantom{-}\frac{1}{6}e^{4} + \frac{1}{6}e^{3} - \frac{4}{3}e^{2} - \frac{2}{3}e - \frac{4}{3}$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{2}e^{4} - 6e^{2} + 2e + 6$
23 $[23, 23, w^{2} - 2]$ $\phantom{-}e^{2} - e - 8$
23 $[23, 23, w^{2} - 3]$ $-1$
23 $[23, 23, -w^{2} + 8]$ $\phantom{-}\frac{1}{2}e^{3} - 4e - 2$
29 $[29, 29, w - 4]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{6}e^{3} - \frac{14}{3}e^{2} + \frac{2}{3}e + \frac{28}{3}$
37 $[37, 37, w^{2} + w - 8]$ $\phantom{-}e^{3} + e^{2} - 10e - 2$
41 $[41, 41, w^{2} + 2w - 4]$ $-\frac{5}{6}e^{4} - \frac{1}{3}e^{3} + \frac{26}{3}e^{2} + \frac{4}{3}e - \frac{16}{3}$
47 $[47, 47, 2w^{2} + w - 8]$ $-\frac{1}{6}e^{4} - \frac{1}{6}e^{3} + \frac{4}{3}e^{2} - \frac{4}{3}e - \frac{8}{3}$
59 $[59, 59, -2w^{2} - 3w + 6]$ $-\frac{5}{6}e^{4} - \frac{5}{6}e^{3} + \frac{26}{3}e^{2} + \frac{10}{3}e - \frac{34}{3}$
61 $[61, 61, -2w - 1]$ $-\frac{1}{3}e^{4} + \frac{2}{3}e^{3} + \frac{14}{3}e^{2} - \frac{23}{3}e - \frac{22}{3}$
67 $[67, 67, -2w - 3]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{7}{6}e^{3} - \frac{14}{3}e^{2} + \frac{26}{3}e + \frac{10}{3}$
79 $[79, 79, 2w^{2} - 9]$ $-\frac{1}{2}e^{3} - 2e^{2} + 2e + 6$
109 $[109, 109, w^{2} + 2w - 6]$ $\phantom{-}\frac{4}{3}e^{4} + \frac{5}{6}e^{3} - \frac{44}{3}e^{2} - \frac{10}{3}e + \frac{58}{3}$
109 $[109, 109, 2w^{2} + w - 14]$ $\phantom{-}\frac{2}{3}e^{4} + \frac{2}{3}e^{3} - \frac{16}{3}e^{2} - \frac{8}{3}e + \frac{2}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, w^{2} - 3]$ $1$