Base field \(\Q(\sqrt{429}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $96$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 16x^{4} + 73x^{2} - 98\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 11]$ | $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} - 11$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{3}{14}e^{5} + \frac{41}{14}e^{3} - \frac{50}{7}e$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{3}{14}e^{5} + \frac{41}{14}e^{3} - \frac{50}{7}e$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}2e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}\frac{2}{7}e^{5} - \frac{25}{7}e^{3} + \frac{55}{7}e$ |
| 17 | $[17, 17, w - 10]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 7$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 7$ |
| 19 | $[19, 19, w + 3]$ | $-\frac{5}{14}e^{5} + \frac{59}{14}e^{3} - \frac{67}{7}e$ |
| 19 | $[19, 19, w + 15]$ | $-\frac{5}{14}e^{5} + \frac{59}{14}e^{3} - \frac{67}{7}e$ |
| 29 | $[29, 29, -2w + 21]$ | $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 21$ |
| 29 | $[29, 29, 5w - 54]$ | $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 21$ |
| 47 | $[47, 47, w + 18]$ | $\phantom{-}e^{5} - 12e^{3} + 29e$ |
| 47 | $[47, 47, w + 28]$ | $\phantom{-}e^{5} - 12e^{3} + 29e$ |
| 59 | $[59, 59, w + 27]$ | $-e^{3} + 6e$ |
| 59 | $[59, 59, w + 31]$ | $-e^{3} + 6e$ |
| 71 | $[71, 71, w + 21]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + 18e$ |
| 71 | $[71, 71, w + 49]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + 18e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |