Base field 3.3.1849.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 14x - 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - x^{2} - 6x + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ | $\phantom{-}e$ |
| 2 | $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ | $\phantom{-}e^{2} - 4$ |
| 2 | $[2, 2, w + 3]$ | $-e^{2} - e + 5$ |
| 11 | $[11, 11, -w^{2} + 3w + 7]$ | $\phantom{-}e^{2} + e - 9$ |
| 11 | $[11, 11, -2w - 1]$ | $-e - 4$ |
| 11 | $[11, 11, -w^{2} + w + 11]$ | $-e^{2}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}0$ |
| 41 | $[41, 41, 2w + 5]$ | $-2e^{2} - 2e + 9$ |
| 41 | $[41, 41, -w^{2} + 3w + 3]$ | $\phantom{-}2e^{2} - 9$ |
| 41 | $[41, 41, -w^{2} + w + 15]$ | $\phantom{-}2e - 1$ |
| 43 | $[43, 43, -3w^{2} + 11w + 11]$ | $\phantom{-}6$ |
| 47 | $[47, 47, -w^{2} - w + 5]$ | $\phantom{-}2e^{2} - 2e - 9$ |
| 47 | $[47, 47, w^{2} - 5w - 3]$ | $\phantom{-}2e^{2} + 4e - 11$ |
| 47 | $[47, 47, -2w^{2} + 4w + 23]$ | $-4e^{2} - 2e + 17$ |
| 59 | $[59, 59, -w^{2} + w + 13]$ | $\phantom{-}e^{2} - e - 8$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $-2e^{2} - e + 5$ |
| 59 | $[59, 59, -2w - 3]$ | $\phantom{-}e^{2} + 2e - 9$ |
| 97 | $[97, 97, 7w^{2} - 11w - 91]$ | $-6e^{2} - 4e + 23$ |
| 97 | $[97, 97, -2w^{2} - 8w - 5]$ | $\phantom{-}4e^{2} - 2e - 21$ |
| 97 | $[97, 97, 5w^{2} - 19w - 15]$ | $\phantom{-}2e^{2} + 6e - 15$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).