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: | $[3, 3, -w + 11]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 68x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 11]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $-3$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{35}{2}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{35}{2}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{33}{2}e$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{1}{4}e^{3} - \frac{33}{2}e$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{35}{3}e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w - 10]$ | $-\frac{1}{24}e^{2} - \frac{17}{12}$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{1}{24}e^{2} + \frac{17}{12}$ |
| 19 | $[19, 19, w + 3]$ | $-\frac{1}{4}e^{3} - \frac{33}{2}e$ |
| 19 | $[19, 19, w + 15]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{33}{2}e$ |
| 29 | $[29, 29, -2w + 21]$ | $\phantom{-}\frac{5}{24}e^{2} + \frac{85}{12}$ |
| 29 | $[29, 29, 5w - 54]$ | $-\frac{5}{24}e^{2} - \frac{85}{12}$ |
| 47 | $[47, 47, w + 18]$ | $-\frac{1}{6}e^{3} - \frac{35}{3}e$ |
| 47 | $[47, 47, w + 28]$ | $-\frac{1}{6}e^{3} - \frac{35}{3}e$ |
| 59 | $[59, 59, w + 27]$ | $-\frac{1}{3}e^{3} - \frac{70}{3}e$ |
| 59 | $[59, 59, w + 31]$ | $-\frac{1}{3}e^{3} - \frac{70}{3}e$ |
| 71 | $[71, 71, w + 21]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{70}{3}e$ |
| 71 | $[71, 71, w + 49]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{70}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 11]$ | $1$ |