Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w]$ |
| 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:
| \(x^{5} - 2x^{4} - 12x^{3} + 13x^{2} + 37x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e^{3} - 9e - 4$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-e^{4} + 3e^{3} + 10e^{2} - 23e - 23$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}2e^{3} + e^{2} - 18e - 14$ |
| 7 | $[7, 7, w]$ | $-1$ |
| 7 | $[7, 7, w + 6]$ | $-e^{4} + e^{3} + 10e^{2} - 6e - 12$ |
| 17 | $[17, 17, w + 8]$ | $-2e^{3} - e^{2} + 18e + 18$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}3e^{4} - 6e^{3} - 28e^{2} + 41e + 44$ |
| 19 | $[19, 19, w - 2]$ | $\phantom{-}2e^{3} + e^{2} - 17e - 20$ |
| 23 | $[23, 23, w + 9]$ | $-2e^{4} + 17e^{2} + 8e$ |
| 23 | $[23, 23, w + 13]$ | $-2e^{3} + 16e + 12$ |
| 37 | $[37, 37, w + 11]$ | $\phantom{-}e^{4} + e^{3} - 9e^{2} - 11e - 2$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}3e^{4} - 8e^{3} - 28e^{2} + 56e + 54$ |
| 59 | $[59, 59, 3w + 10]$ | $-5e^{3} - e^{2} + 42e + 28$ |
| 59 | $[59, 59, 3w - 13]$ | $\phantom{-}e^{4} - 4e^{3} - 11e^{2} + 33e + 36$ |
| 73 | $[73, 73, w + 15]$ | $-2e^{3} - e^{2} + 20e + 14$ |
| 73 | $[73, 73, w + 57]$ | $-e^{4} + 9e^{2} + 4e + 6$ |
| 89 | $[89, 89, -w - 10]$ | $-4e^{4} + 9e^{3} + 38e^{2} - 63e - 70$ |
| 89 | $[89, 89, w - 11]$ | $-5e^{4} + 3e^{3} + 46e^{2} - 10e - 30$ |
| 97 | $[97, 97, w + 22]$ | $\phantom{-}11e^{3} + 3e^{2} - 95e - 70$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $1$ |