Base field 3.3.1304.1
Generator \(w\), with minimal polynomial \(x^{3} - 11x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[3, 3, -w^{2} + 3w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 8x^{3} - 6x^{2} + 7x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{7}{2}e^{2} + \frac{5}{2}e - 1$ |
| 3 | $[3, 3, -w^{2} + 3w + 1]$ | $\phantom{-}1$ |
| 9 | $[9, 3, w^{2} + w - 7]$ | $\phantom{-}\frac{1}{2}e^{4} - 4e^{2} + e + \frac{5}{2}$ |
| 11 | $[11, 11, 2w^{2} - 21]$ | $-e^{4} - e^{3} + 8e^{2} + 5e - 5$ |
| 17 | $[17, 17, -\frac{1}{2}w^{2} + \frac{5}{2}w]$ | $\phantom{-}\frac{1}{2}e^{4} + e^{3} - 4e^{2} - 6e + \frac{9}{2}$ |
| 19 | $[19, 19, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}e^{4} + e^{3} - 8e^{2} - 7e + 5$ |
| 37 | $[37, 37, w^{2} - w - 13]$ | $-\frac{1}{2}e^{4} + 4e^{2} + e + \frac{3}{2}$ |
| 37 | $[37, 37, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $\phantom{-}\frac{1}{2}e^{4} + 2e^{3} - 2e^{2} - 13e + \frac{1}{2}$ |
| 37 | $[37, 37, \frac{5}{2}w^{2} - \frac{17}{2}w - 2]$ | $\phantom{-}e^{3} - e^{2} - 7e + 3$ |
| 47 | $[47, 47, -\frac{3}{2}w^{2} + \frac{11}{2}w]$ | $\phantom{-}e^{4} - 7e^{2} - 2e - 2$ |
| 53 | $[53, 53, w^{2} - w - 7]$ | $-\frac{3}{2}e^{4} - e^{3} + 12e^{2} + 8e - \frac{11}{2}$ |
| 59 | $[59, 59, 2w - 1]$ | $-e^{4} + e^{3} + 8e^{2} - 9e - 7$ |
| 61 | $[61, 61, -\frac{3}{2}w^{2} + \frac{3}{2}w + 20]$ | $\phantom{-}2e^{4} - 17e^{2} + 15$ |
| 67 | $[67, 67, w^{2} - 3w - 3]$ | $-2e^{4} - 2e^{3} + 17e^{2} + 10e - 13$ |
| 71 | $[71, 71, w^{2} - w - 1]$ | $-2e + 2$ |
| 73 | $[73, 73, 3w^{2} - w - 33]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 6e^{2} + 10e + \frac{17}{2}$ |
| 79 | $[79, 79, w^{2} - w - 11]$ | $\phantom{-}2e - 2$ |
| 79 | $[79, 79, w^{2} - 3w + 1]$ | $\phantom{-}e^{4} - e^{3} - 8e^{2} + 5e + 7$ |
| 79 | $[79, 79, -2w - 5]$ | $\phantom{-}2e^{3} - 16e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{2} + 3w + 1]$ | $-1$ |