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 | $[109, 109, 2w^{2} + w - 14]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{2}{3}e^{3} - \frac{16}{3}e^{2} - \frac{8}{3}e + \frac{2}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, w^{2} - 3]$ | $1$ |