Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 9x^{3} - x^{2} + 12x - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{5}{3}e^{4} + 3e^{3} - 13e^{2} - \frac{35}{3}e + \frac{41}{3}$ |
| 11 | $[11, 11, -3w - 17]$ | $-e^{4} - 2e^{3} + 7e^{2} + 8e - 6$ |
| 11 | $[11, 11, 3w - 20]$ | $-e^{4} - 2e^{3} + 7e^{2} + 8e - 6$ |
| 13 | $[13, 13, 2w - 13]$ | $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 9e + 9$ |
| 13 | $[13, 13, 2w + 11]$ | $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 9e + 9$ |
| 17 | $[17, 17, w + 7]$ | $-3e^{4} - 5e^{3} + 23e^{2} + 18e - 22$ |
| 17 | $[17, 17, -w + 8]$ | $-3e^{4} - 5e^{3} + 23e^{2} + 18e - 22$ |
| 19 | $[19, 19, -w - 4]$ | $\phantom{-}\frac{1}{3}e^{4} - 4e^{2} + \frac{5}{3}e + \frac{19}{3}$ |
| 19 | $[19, 19, -w + 5]$ | $\phantom{-}\frac{1}{3}e^{4} - 4e^{2} + \frac{5}{3}e + \frac{19}{3}$ |
| 25 | $[25, 5, 5]$ | $-\frac{8}{3}e^{4} - 4e^{3} + 21e^{2} + \frac{41}{3}e - \frac{41}{3}$ |
| 31 | $[31, 31, -6w - 35]$ | $-\frac{7}{3}e^{4} - 3e^{3} + 20e^{2} + \frac{25}{3}e - \frac{58}{3}$ |
| 31 | $[31, 31, -6w + 41]$ | $-\frac{7}{3}e^{4} - 3e^{3} + 20e^{2} + \frac{25}{3}e - \frac{58}{3}$ |
| 37 | $[37, 37, -w - 1]$ | $-\frac{1}{3}e^{4} + 4e^{2} + \frac{4}{3}e - \frac{10}{3}$ |
| 37 | $[37, 37, w - 2]$ | $-\frac{1}{3}e^{4} + 4e^{2} + \frac{4}{3}e - \frac{10}{3}$ |
| 47 | $[47, 47, 3w + 16]$ | $\phantom{-}4e^{4} + 7e^{3} - 31e^{2} - 24e + 28$ |
| 47 | $[47, 47, -3w + 19]$ | $\phantom{-}4e^{4} + 7e^{3} - 31e^{2} - 24e + 28$ |
| 49 | $[49, 7, -7]$ | $-3e^{4} - 5e^{3} + 24e^{2} + 21e - 18$ |
| 67 | $[67, 67, 3w - 22]$ | $\phantom{-}3e^{4} + 6e^{3} - 22e^{2} - 26e + 17$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).