Base field 3.3.621.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[16, 4, -w^{2} - w + 1]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 2x^{4} - 7x^{3} - 12x^{2} + 9x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w]$ | $-\frac{1}{3}e^{4} + \frac{1}{3}e^{3} + \frac{7}{3}e^{2} - 2e - 3$ |
4 | $[4, 2, -w^{2} + w + 5]$ | $\phantom{-}0$ |
7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{10}{3}e^{2} + e + 5$ |
19 | $[19, 19, -2w^{2} + w + 10]$ | $\phantom{-}\frac{4}{3}e^{4} + \frac{5}{3}e^{3} - \frac{25}{3}e^{2} - 7e + 5$ |
23 | $[23, 23, -w^{2} + 8]$ | $-e^{3} + 5e - 6$ |
23 | $[23, 23, -w^{2} + 2]$ | $-e^{2} - e$ |
29 | $[29, 29, -w^{2} + 2w + 4]$ | $-2e^{4} - e^{3} + 13e^{2} + 4e - 12$ |
37 | $[37, 37, w^{2} - 2w - 8]$ | $-\frac{2}{3}e^{4} - \frac{1}{3}e^{3} + \frac{20}{3}e^{2} - 13$ |
41 | $[41, 41, 4w^{2} - 3w - 20]$ | $-2e^{3} - e^{2} + 11e$ |
43 | $[43, 43, -w - 4]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{10}{3}e^{2} + 2e + 2$ |
47 | $[47, 47, 2w - 1]$ | $\phantom{-}e^{3} + e^{2} - 8e - 6$ |
49 | $[49, 7, -2w^{2} + 3w + 4]$ | $-\frac{2}{3}e^{4} - \frac{1}{3}e^{3} + \frac{17}{3}e^{2} + 2e - 4$ |
59 | $[59, 59, 2w^{2} - 13]$ | $-2e^{3} + 11e - 3$ |
61 | $[61, 61, -3w^{2} + 4w + 10]$ | $-\frac{2}{3}e^{4} + \frac{2}{3}e^{3} + \frac{20}{3}e^{2} - 3e - 13$ |
67 | $[67, 67, 2w^{2} - 2w - 7]$ | $\phantom{-}\frac{7}{3}e^{4} + \frac{2}{3}e^{3} - \frac{43}{3}e^{2} + 14$ |
71 | $[71, 71, -3w - 4]$ | $-2e^{3} - 3e^{2} + 9e + 6$ |
79 | $[79, 79, 2w^{2} - 3w - 8]$ | $-\frac{5}{3}e^{4} + \frac{5}{3}e^{3} + \frac{35}{3}e^{2} - 8e - 7$ |
83 | $[83, 83, 2w^{2} - w - 14]$ | $\phantom{-}e^{4} + e^{3} - 4e^{2} - 2e - 6$ |
83 | $[83, 83, -4w^{2} + 3w + 22]$ | $-e^{4} + 7e^{2} + e - 15$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.