Base field 3.3.169.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[53,53,-w^{2} - w + 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 4x^{3} - 5x^{2} + 18x + 17\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{2}{3}e^{3} - 2e^{2} - \frac{4}{3}e + \frac{8}{3}$ |
5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 1]$ | $-e^{2} + 2e + 4$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{3} - 2e^{2} + \frac{4}{3}e + \frac{16}{3}$ |
13 | $[13, 13, -w^{2} + 3]$ | $-\frac{2}{3}e^{3} + e^{2} + \frac{10}{3}e + \frac{7}{3}$ |
27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e - \frac{14}{3}$ |
31 | $[31, 31, -2w^{2} + 3w + 3]$ | $\phantom{-}\frac{2}{3}e^{3} - e^{2} - \frac{22}{3}e + \frac{8}{3}$ |
31 | $[31, 31, -w^{2} + 5]$ | $-\frac{4}{3}e^{3} + 5e^{2} + \frac{8}{3}e - \frac{31}{3}$ |
31 | $[31, 31, -w^{2} + 3w + 4]$ | $-2e^{2} + 3e + 8$ |
47 | $[47, 47, 2w - 3]$ | $-2e^{2} + 6e + 6$ |
47 | $[47, 47, 2w^{2} - 4w - 7]$ | $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} - \frac{23}{3}e - \frac{20}{3}$ |
47 | $[47, 47, 2w^{2} - 2w - 3]$ | $-\frac{2}{3}e^{3} - 2e^{2} + \frac{28}{3}e + \frac{52}{3}$ |
53 | $[53, 53, 3w^{2} - 4w - 8]$ | $-2e^{3} + 4e^{2} + 10e - 4$ |
53 | $[53, 53, 4w^{2} - 6w - 11]$ | $-\frac{4}{3}e^{3} + 6e^{2} - \frac{4}{3}e - \frac{40}{3}$ |
53 | $[53, 53, 3w^{2} - 5w - 6]$ | $\phantom{-}1$ |
73 | $[73, 73, w^{2} - 4w - 4]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e + \frac{4}{3}$ |
73 | $[73, 73, 2w^{2} - w - 8]$ | $\phantom{-}\frac{4}{3}e^{3} - 6e^{2} + \frac{4}{3}e + \frac{34}{3}$ |
73 | $[73, 73, 3w^{2} - 5w - 5]$ | $\phantom{-}e^{3} - 2e^{2} - 7e - 2$ |
79 | $[79, 79, -3w^{2} + 5w + 4]$ | $\phantom{-}2e^{3} - 4e^{2} - 8e - 4$ |
79 | $[79, 79, 2w^{2} - w - 9]$ | $\phantom{-}2e^{2} - 6e - 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$53$ | $[53,53,-w^{2} - w + 3]$ | $-1$ |