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: | $[5, 5, w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 7x^{4} + 11x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $\phantom{-}e^{5} + 6e^{3} + 6e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{2}e^{5} + 3e^{3} + \frac{7}{2}e$ |
| 11 | $[11, 11, 10w + 4]$ | $-e^{5} - 7e^{3} - 12e$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $-e^{5} - 7e^{3} - 12e$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}e^{2} + 1$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $\phantom{-}3e^{5} + 19e^{3} + 26e$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $\phantom{-}e^{5} + 6e^{3} + 5e$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $-e^{5} - 7e^{3} - 10e$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $-e^{4} - 4e^{2} - 1$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $\phantom{-}3e^{5} + 22e^{3} + 33e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}2$ |
| 29 | $[29, 29, w + 7]$ | $-2e^{5} - 12e^{3} - 14e$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $\phantom{-}e^{5} + 5e^{3} + 2e$ |
| 43 | $[43, 43, w^{2} - 11]$ | $-2e^{4} - 12e^{2} - 6$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $\phantom{-}e^{4} + 2e^{2} - 7$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}e^{4} + 8e^{2} + 9$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $\phantom{-}2e^{4} + 11e^{2} + 11$ |
| 79 | $[79, 79, w^{2} + 37]$ | $\phantom{-}4e^{5} + 23e^{3} + 21e$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $\phantom{-}e^{4} + 3e^{2} + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $-\frac{1}{2}e^{5} - 3e^{3} - \frac{7}{2}e$ |