Base field 3.3.1593.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[15, 15, w - 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 3x^{2} - 7x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{2} - 2w - 4]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 3]$ | $-1$ |
| 7 | $[7, 7, -w^{2} + 2w + 3]$ | $-e - 2$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{2}e^{2} - 2e + \frac{5}{2}$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $-\frac{1}{2}e^{2} - e + \frac{1}{2}$ |
| 17 | $[17, 17, w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} + e - \frac{11}{2}$ |
| 25 | $[25, 5, -w^{2} - w + 3]$ | $\phantom{-}e^{2} + 4e - 3$ |
| 29 | $[29, 29, w^{2} - 2w - 6]$ | $\phantom{-}\frac{3}{2}e^{2} + 4e - \frac{7}{2}$ |
| 31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}e^{2} + 2e - 7$ |
| 37 | $[37, 37, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} + 3e - \frac{5}{2}$ |
| 41 | $[41, 41, w^{2} - 8]$ | $-\frac{5}{2}e^{2} - 7e + \frac{15}{2}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{2}e^{2} + 2e - \frac{13}{2}$ |
| 53 | $[53, 53, 2w^{2} - 5w - 4]$ | $-2e - 6$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{3}{2}e^{2} + 5e - \frac{29}{2}$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $-\frac{3}{2}e^{2} - 6e + \frac{23}{2}$ |
| 61 | $[61, 61, -w^{2} + 2w + 12]$ | $\phantom{-}\frac{1}{2}e^{2} + 5e - \frac{1}{2}$ |
| 67 | $[67, 67, -2w^{2} + 6w + 3]$ | $-\frac{3}{2}e^{2} - 5e + \frac{11}{2}$ |
| 71 | $[71, 71, w^{2} - w - 11]$ | $\phantom{-}2e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $-1$ |
| $5$ | $[5, 5, w^{2} - 2w - 4]$ | $-1$ |