Base field \(\Q(\sqrt{209}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 52\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,-4w - 27]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 13x^{8} + 48x^{6} - 43x^{4} + 12x^{2} - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w - 74]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -11w + 85]$ | $\phantom{-}5e^{9} - 64e^{7} + 227e^{5} - 168e^{3} + 24e$ |
| 5 | $[5, 5, 4w - 31]$ | $-e^{8} + 13e^{6} - 48e^{4} + 42e^{2} - 9$ |
| 5 | $[5, 5, -4w - 27]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}3e^{8} - 38e^{6} + 132e^{4} - 90e^{2} + 10$ |
| 11 | $[11, 11, -70w - 471]$ | $\phantom{-}e^{8} - 13e^{6} + 48e^{4} - 43e^{2} + 10$ |
| 13 | $[13, 13, -2w - 13]$ | $-8e^{9} + 102e^{7} - 359e^{5} + 258e^{3} - 35e$ |
| 13 | $[13, 13, -2w + 15]$ | $-10e^{9} + 127e^{7} - 442e^{5} + 299e^{3} - 38e$ |
| 19 | $[19, 19, 92w - 711]$ | $-4e^{9} + 51e^{7} - 179e^{5} + 125e^{3} - 11e$ |
| 23 | $[23, 23, -26w + 201]$ | $\phantom{-}6e^{8} - 77e^{6} + 274e^{4} - 204e^{2} + 30$ |
| 23 | $[23, 23, -26w - 175]$ | $-4e^{8} + 51e^{6} - 179e^{4} + 125e^{2} - 18$ |
| 29 | $[29, 29, 18w - 139]$ | $-2e^{9} + 27e^{7} - 108e^{5} + 123e^{3} - 36e$ |
| 29 | $[29, 29, 18w + 121]$ | $\phantom{-}15e^{9} - 192e^{7} + 682e^{5} - 512e^{3} + 85e$ |
| 41 | $[41, 41, -10w - 67]$ | $\phantom{-}23e^{9} - 294e^{7} + 1041e^{5} - 772e^{3} + 128e$ |
| 41 | $[41, 41, 10w - 77]$ | $\phantom{-}4e^{9} - 50e^{7} + 167e^{5} - 89e^{3} + 6e$ |
| 47 | $[47, 47, 2w - 17]$ | $-2e^{8} + 26e^{6} - 96e^{4} + 85e^{2} - 22$ |
| 47 | $[47, 47, 2w + 15]$ | $\phantom{-}8e^{8} - 103e^{6} + 370e^{4} - 289e^{2} + 41$ |
| 49 | $[49, 7, -7]$ | $-2e^{8} + 26e^{6} - 97e^{4} + 92e^{2} - 24$ |
| 79 | $[79, 79, 40w - 309]$ | $-9e^{9} + 116e^{7} - 419e^{5} + 337e^{3} - 55e$ |
| 79 | $[79, 79, 40w + 269]$ | $-19e^{9} + 243e^{7} - 862e^{5} + 648e^{3} - 122e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-4w - 27]$ | $-1$ |