Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); 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: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 30x^{8} + 315x^{6} - 1350x^{4} + 2025x^{2} - 700\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{40}e^{8} - \frac{3}{5}e^{6} + \frac{9}{2}e^{4} - \frac{91}{8}e^{2} + \frac{15}{2}$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{1}{5}e^{5} - 3e^{3} + 9e$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 4]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 18]$ | $\phantom{-}0$ |
| 25 | $[25, 5, 5]$ | $-\frac{1}{5}e^{6} + 4e^{4} - 21e^{2} + 18$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}0$ |
| 29 | $[29, 29, w + 27]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{1}{10}e^{7} - \frac{21}{10}e^{5} + \frac{23}{2}e^{3} - 9e$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{1}{10}e^{7} - \frac{21}{10}e^{5} + \frac{23}{2}e^{3} - 9e$ |
| 43 | $[43, 43, -w - 11]$ | $-\frac{1}{20}e^{6} + \frac{1}{4}e^{4} + \frac{15}{4}e^{2} - 9$ |
| 43 | $[43, 43, w - 12]$ | $-\frac{1}{20}e^{6} + \frac{1}{4}e^{4} + \frac{15}{4}e^{2} - 9$ |
| 47 | $[47, 47, -w - 6]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w - 7]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -w - 5]$ | $\phantom{-}0$ |
| 59 | $[59, 59, w - 6]$ | $\phantom{-}0$ |
| 61 | $[61, 61, w + 16]$ | $-\frac{1}{20}e^{9} + \frac{27}{20}e^{7} - \frac{243}{20}e^{5} + \frac{81}{2}e^{3} - 32e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).