Base field \(\Q(\sqrt{61}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 15\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[180, 90, -8w - 30]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $55$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 3x^{2} - 9x + 26\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 3]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w + 4]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 5]$ | $-1$ |
| 5 | $[5, 5, -w - 4]$ | $-e^{2} + 10$ |
| 13 | $[13, 13, -w - 1]$ | $-2e^{2} - e + 20$ |
| 13 | $[13, 13, w - 2]$ | $\phantom{-}e^{2} - 8$ |
| 19 | $[19, 19, 3w - 14]$ | $-2e^{2} + e + 18$ |
| 19 | $[19, 19, -3w - 11]$ | $\phantom{-}2e^{2} - 18$ |
| 41 | $[41, 41, -w - 7]$ | $-3e^{2} + 2e + 22$ |
| 41 | $[41, 41, w - 8]$ | $\phantom{-}2e - 2$ |
| 47 | $[47, 47, 3w - 11]$ | $-e - 2$ |
| 47 | $[47, 47, -3w - 8]$ | $\phantom{-}0$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e^{2} - 12$ |
| 61 | $[61, 61, 2w - 1]$ | $\phantom{-}3e^{2} - 2e - 26$ |
| 73 | $[73, 73, -3w + 16]$ | $\phantom{-}2e^{2} + 2e - 14$ |
| 73 | $[73, 73, 3w + 13]$ | $-2e + 4$ |
| 83 | $[83, 83, 2w - 13]$ | $\phantom{-}12$ |
| 83 | $[83, 83, -2w - 11]$ | $\phantom{-}2e^{2} - 14$ |
| 97 | $[97, 97, 7w + 22]$ | $-2e^{2} + 3e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 3]$ | $-1$ |
| $4$ | $[4, 2, 2]$ | $-1$ |
| $5$ | $[5, 5, w - 5]$ | $1$ |