Base field 3.3.621.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -2w^{2} + w + 10]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2x - 1\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + w + 5]$ | $-2$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}e + 1$ |
| 19 | $[19, 19, -2w^{2} + w + 10]$ | $-1$ |
| 23 | $[23, 23, -w^{2} + 8]$ | $-5e - 3$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}e$ |
| 29 | $[29, 29, -w^{2} + 2w + 4]$ | $\phantom{-}3e + 8$ |
| 37 | $[37, 37, w^{2} - 2w - 8]$ | $-2e + 6$ |
| 41 | $[41, 41, 4w^{2} - 3w - 20]$ | $\phantom{-}e - 5$ |
| 43 | $[43, 43, -w - 4]$ | $\phantom{-}2e + 1$ |
| 47 | $[47, 47, 2w - 1]$ | $-3e - 7$ |
| 49 | $[49, 7, -2w^{2} + 3w + 4]$ | $\phantom{-}7e + 10$ |
| 59 | $[59, 59, 2w^{2} - 13]$ | $-4e - 12$ |
| 61 | $[61, 61, -3w^{2} + 4w + 10]$ | $-6e - 5$ |
| 67 | $[67, 67, 2w^{2} - 2w - 7]$ | $-15$ |
| 71 | $[71, 71, -3w - 4]$ | $\phantom{-}2e + 9$ |
| 79 | $[79, 79, 2w^{2} - 3w - 8]$ | $-3e + 3$ |
| 83 | $[83, 83, 2w^{2} - w - 14]$ | $\phantom{-}6e + 3$ |
| 83 | $[83, 83, -4w^{2} + 3w + 22]$ | $\phantom{-}6e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -2w^{2} + w + 10]$ | $1$ |