Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 4, -w - 8]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 12x^{8} + 46x^{6} - 61x^{4} + 25x^{2} - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -4w + 37]$ | $-e^{8} + 12e^{6} - 45e^{4} + 53e^{2} - 12$ |
| 7 | $[7, 7, w + 2]$ | $-3e^{9} + 35e^{7} - 127e^{5} + 146e^{3} - 36e$ |
| 7 | $[7, 7, w + 4]$ | $-e$ |
| 9 | $[9, 3, 3]$ | $-e^{8} + 12e^{6} - 45e^{4} + 54e^{2} - 14$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}2e^{9} - 23e^{7} + 81e^{5} - 86e^{3} + 18e$ |
| 17 | $[17, 17, w + 10]$ | $\phantom{-}4e^{9} - 47e^{7} + 171e^{5} - 192e^{3} + 38e$ |
| 19 | $[19, 19, -2w + 19]$ | $-e^{6} + 9e^{4} - 22e^{2} + 10$ |
| 19 | $[19, 19, -2w - 17]$ | $\phantom{-}2e^{8} - 23e^{6} + 81e^{4} - 86e^{2} + 16$ |
| 23 | $[23, 23, w + 5]$ | $-7e^{9} + 82e^{7} - 298e^{5} + 339e^{3} - 79e$ |
| 23 | $[23, 23, w + 17]$ | $\phantom{-}2e^{9} - 23e^{7} + 81e^{5} - 87e^{3} + 20e$ |
| 37 | $[37, 37, w + 1]$ | $-4e^{9} + 47e^{7} - 172e^{5} + 200e^{3} - 51e$ |
| 37 | $[37, 37, w + 35]$ | $\phantom{-}4e^{9} - 47e^{7} + 172e^{5} - 202e^{3} + 59e$ |
| 41 | $[41, 41, -22w + 203]$ | $\phantom{-}4e^{8} - 47e^{6} + 173e^{4} - 204e^{2} + 45$ |
| 41 | $[41, 41, -6w + 55]$ | $\phantom{-}e^{6} - 11e^{4} + 32e^{2} - 15$ |
| 43 | $[43, 43, w + 20]$ | $-2e^{9} + 23e^{7} - 80e^{5} + 78e^{3} - 3e$ |
| 43 | $[43, 43, w + 22]$ | $\phantom{-}6e^{9} - 71e^{7} + 262e^{5} - 306e^{3} + 69e$ |
| 53 | $[53, 53, w + 13]$ | $\phantom{-}e^{9} - 12e^{7} + 47e^{5} - 66e^{3} + 26e$ |
| 53 | $[53, 53, w + 39]$ | $\phantom{-}3e^{9} - 34e^{7} + 117e^{5} - 118e^{3} + 20e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |