Base field 3.3.837.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[15, 15, -w^{2} + 4]$ |
| Dimension: | $4$ |
| 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:
| \(x^{4} - 11x^{2} + 26\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-1$ |
| 4 | $[4, 2, w^{2} + w - 3]$ | $-e^{2} + 6$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -2w - 5]$ | $-e^{2} + 7$ |
| 25 | $[25, 5, -w^{2} - 2w + 2]$ | $\phantom{-}e^{3} - e^{2} - 5e + 7$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $-e^{3} - e^{2} + 7e + 7$ |
| 31 | $[31, 31, -2w + 1]$ | $-e^{2} - 2e + 7$ |
| 37 | $[37, 37, 2w + 3]$ | $-2e + 4$ |
| 41 | $[41, 41, -w - 4]$ | $\phantom{-}e^{3} - 5e - 2$ |
| 43 | $[43, 43, 2w^{2} - 2w - 7]$ | $-e^{3} - e^{2} + 9e + 5$ |
| 47 | $[47, 47, -2w^{2} - w + 8]$ | $-2e - 2$ |
| 53 | $[53, 53, 3w^{2} - 6w - 2]$ | $-e^{3} - 2e^{2} + 9e + 8$ |
| 53 | $[53, 53, -2w^{2} + 3w + 18]$ | $\phantom{-}e^{3} - 5e - 6$ |
| 53 | $[53, 53, 2w - 3]$ | $\phantom{-}e^{3} + 4e^{2} - 7e - 20$ |
| 59 | $[59, 59, 2w^{2} - 3w - 4]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 8$ |
| 61 | $[61, 61, w^{2} - 2w - 4]$ | $-e^{3} + e^{2} + 7e - 5$ |
| 71 | $[71, 71, 4w + 9]$ | $\phantom{-}e^{3} - 5e + 4$ |
| 73 | $[73, 73, 2w^{2} - 9]$ | $\phantom{-}2e^{3} - 3e^{2} - 10e + 21$ |
| 79 | $[79, 79, w^{2} - 4w + 2]$ | $\phantom{-}3e^{2} - 2e - 13$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $1$ |
| $5$ | $[5, 5, -w + 2]$ | $-1$ |