Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[4, 4, -w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 14x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{15}{2}e$ |
| 11 | $[11, 11, 10w + 4]$ | $\phantom{-}e^{3} + 13e$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 1]$ | $-\frac{1}{2}e^{2} - \frac{11}{2}$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $\phantom{-}e^{3} + 15e$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{3}{2}e^{3} - \frac{41}{2}e$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $\phantom{-}2e^{3} + 28e$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $-6$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $-\frac{3}{2}e^{3} - \frac{37}{2}e$ |
| 27 | $[27, 3, -3]$ | $-e^{2} - 5$ |
| 29 | $[29, 29, w + 7]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{19}{2}e$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $-e^{3} - 15e$ |
| 43 | $[43, 43, w^{2} - 11]$ | $-e^{2} - 3$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $-e^{2} - 11$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-e^{2} - 13$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $\phantom{-}\frac{3}{2}e^{2} + \frac{21}{2}$ |
| 79 | $[79, 79, w^{2} + 37]$ | $\phantom{-}2e^{3} + 28e$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{15}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2}]$ | $1$ |