Base field 3.3.1373.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[15, 15, w^{2} + 2w]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 3x^{2} - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}1$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $-e^{2} - 2e + 1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $\phantom{-}e - 2$ |
| 13 | $[13, 13, -w + 2]$ | $-2e^{2} - 3e + 1$ |
| 25 | $[25, 5, w^{2} - 8]$ | $\phantom{-}3e^{2} + 6e - 5$ |
| 29 | $[29, 29, 2w + 3]$ | $\phantom{-}2e^{2} + e - 3$ |
| 37 | $[37, 37, w + 4]$ | $\phantom{-}3e^{2} + 3e - 5$ |
| 37 | $[37, 37, -3w^{2} + 2w + 24]$ | $\phantom{-}5e^{2} + 10e - 5$ |
| 37 | $[37, 37, w^{2} + 2w - 2]$ | $-2e^{2} - 5e - 4$ |
| 47 | $[47, 47, w^{2} - 2]$ | $\phantom{-}2e^{2} + e - 6$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $-4e^{2} - 4e + 9$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}4e^{2} - 11$ |
| 71 | $[71, 71, 2w - 1]$ | $-8e^{2} - 8e + 18$ |
| 71 | $[71, 71, -w^{2} + 4w + 2]$ | $\phantom{-}6e^{2} + 5e - 12$ |
| 71 | $[71, 71, -w^{2} + 4w - 2]$ | $\phantom{-}7e^{2} + 14e - 9$ |
| 73 | $[73, 73, -w^{2} + 4w + 4]$ | $\phantom{-}2e^{2} + 9e - 2$ |
| 79 | $[79, 79, -2w + 7]$ | $\phantom{-}2e^{2} - 3e - 8$ |
| 83 | $[83, 83, -2w^{2} + 13]$ | $\phantom{-}5e^{2} + 14e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $-1$ |
| $5$ | $[5, 5, w]$ | $-1$ |