Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10, 10, -9w + 80]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $53$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 3x^{2} - 12x - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $-1$ |
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -76w + 675]$ | $-1$ |
| 5 | $[5, 5, 76w + 599]$ | $-e^{3} - e^{2} + 5e + 3$ |
| 7 | $[7, 7, -8w - 63]$ | $-e^{3} - e^{2} + 4e + 2$ |
| 7 | $[7, 7, -8w + 71]$ | $-e + 1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{3} + e^{2} - 6e - 6$ |
| 17 | $[17, 17, 42w + 331]$ | $\phantom{-}e^{2} + e - 4$ |
| 17 | $[17, 17, 42w - 373]$ | $\phantom{-}e^{3} + e^{2} - 4e - 4$ |
| 29 | $[29, 29, -6w - 47]$ | $\phantom{-}2e - 4$ |
| 29 | $[29, 29, 6w - 53]$ | $-e^{3} + 3e - 4$ |
| 31 | $[31, 31, 10w + 79]$ | $\phantom{-}e^{3} + e^{2} - 5e - 5$ |
| 31 | $[31, 31, -10w + 89]$ | $\phantom{-}3e^{3} + 5e^{2} - 14e - 14$ |
| 43 | $[43, 43, 2w - 19]$ | $-3e^{3} - 3e^{2} + 12e + 6$ |
| 43 | $[43, 43, -2w - 17]$ | $\phantom{-}2e^{3} + 5e^{2} - 9e - 18$ |
| 53 | $[53, 53, 194w + 1529]$ | $-e^{2} - e + 4$ |
| 53 | $[53, 53, -194w + 1723]$ | $-e^{3} - 3e^{2} + 2e + 4$ |
| 59 | $[59, 59, -110w - 867]$ | $-2e^{3} - e^{2} + 10e + 1$ |
| 59 | $[59, 59, 110w - 977]$ | $\phantom{-}2e^{3} + 6e^{2} - 6e - 14$ |
| 79 | $[79, 79, 650w - 5773]$ | $\phantom{-}4e^{3} + 8e^{2} - 15e - 21$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 8]$ | $1$ |
| $5$ | $[5, 5, -76w + 675]$ | $1$ |