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 | $[109, 109, 2w^{2} + w - 14]$ | $-\frac{74}{13}e^{5} - \frac{2}{13}e^{4} + \frac{713}{13}e^{3} - \frac{618}{13}e^{2} - \frac{487}{13}e + \frac{265}{13}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, w^{2} - 2]$ | $1$ |