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: | $[1, 1, 1]$ |
| Dimension: | $10$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 70x^{8} + 1715x^{6} - 17150x^{4} + 60025x^{2} - 35152\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 11]$ | $-\frac{1}{1404}e^{8} + \frac{14}{351}e^{6} - \frac{245}{351}e^{4} + \frac{5561}{1404}e^{2} - \frac{112}{27}$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{5}{936}e^{6} - \frac{227}{936}e^{4} + \frac{2681}{936}e^{2} - \frac{49}{9}$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{1}{26}e^{5} + \frac{35}{26}e^{3} - \frac{245}{26}e$ |
| 17 | $[17, 17, w - 10]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{1}{234}e^{7} - \frac{49}{234}e^{5} + \frac{709}{234}e^{3} - \frac{1442}{117}e$ |
| 19 | $[19, 19, w + 15]$ | $\phantom{-}\frac{1}{234}e^{7} - \frac{49}{234}e^{5} + \frac{709}{234}e^{3} - \frac{1442}{117}e$ |
| 29 | $[29, 29, -2w + 21]$ | $\phantom{-}0$ |
| 29 | $[29, 29, 5w - 54]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w + 18]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w + 28]$ | $\phantom{-}0$ |
| 59 | $[59, 59, w + 27]$ | $\phantom{-}0$ |
| 59 | $[59, 59, w + 31]$ | $\phantom{-}0$ |
| 71 | $[71, 71, w + 21]$ | $\phantom{-}0$ |
| 71 | $[71, 71, w + 49]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).