Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[14, 14, w - 1]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 7x^{4} + 6x^{3} + 39x^{2} - 64x + 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $-2e^{4} + 6e^{3} + 13e^{2} - 28e + 8$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $-2e^{4} + 7e^{3} + 11e^{2} - 36e + 14$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $-e^{2} + e + 6$ |
| 19 | $[19, 19, -w + 2]$ | $-e^{4} + 3e^{3} + 7e^{2} - 15e + 2$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $\phantom{-}e^{3} - 3e^{2} - 6e + 12$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $-e^{4} + 3e^{3} + 6e^{2} - 12e + 8$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}e^{3} - 3e^{2} - 6e + 10$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $\phantom{-}4e^{4} - 12e^{3} - 26e^{2} + 55e - 12$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $-e$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $\phantom{-}e^{4} - 4e^{3} - 5e^{2} + 24e - 12$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $-e^{4} + 4e^{3} + 5e^{2} - 24e + 14$ |
| 47 | $[47, 47, -2w + 7]$ | $-3e^{4} + 8e^{3} + 22e^{2} - 34e$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $\phantom{-}5e^{4} - 17e^{3} - 29e^{2} + 89e - 30$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}5e^{4} - 17e^{3} - 29e^{2} + 86e - 28$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $-2e^{4} + 4e^{3} + 18e^{2} - 15e - 4$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $\phantom{-}2e^{4} - 8e^{3} - 8e^{2} + 40e - 22$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $\phantom{-}e^{4} - 2e^{3} - 10e^{2} + 8e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 1]$ | $1$ |
| $7$ | $[7, 7, -w^{2} + 2w + 6]$ | $-1$ |