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: | $[2, 2, w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} + 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -4w + 37]$ | $\phantom{-}e^{2} - e - 1$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}e^{3} - 2e^{2} - 2e + 4$ |
| 7 | $[7, 7, w + 4]$ | $-3e^{3} + 6e^{2} + 5e - 6$ |
| 9 | $[9, 3, 3]$ | $-e^{2} + 2e$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}e^{3} - 4e^{2} + 8$ |
| 17 | $[17, 17, w + 10]$ | $\phantom{-}2e^{3} - 2e^{2} - 5e + 2$ |
| 19 | $[19, 19, -2w + 19]$ | $\phantom{-}e^{3} + e^{2} - 6e + 1$ |
| 19 | $[19, 19, -2w - 17]$ | $-4e^{3} + 7e^{2} + 5e - 6$ |
| 23 | $[23, 23, w + 5]$ | $\phantom{-}3e^{2} - 2e - 4$ |
| 23 | $[23, 23, w + 17]$ | $\phantom{-}2e^{2} - 4e - 1$ |
| 37 | $[37, 37, w + 1]$ | $-3e + 4$ |
| 37 | $[37, 37, w + 35]$ | $\phantom{-}4e^{3} - 6e^{2} - 7e + 5$ |
| 41 | $[41, 41, -22w + 203]$ | $\phantom{-}2e^{3} - 7e^{2} + 5e + 9$ |
| 41 | $[41, 41, -6w + 55]$ | $-4e^{3} + 9e^{2} + 2e - 8$ |
| 43 | $[43, 43, w + 20]$ | $-6e^{3} + 12e^{2} + 10e - 11$ |
| 43 | $[43, 43, w + 22]$ | $-2e^{3} + 5e^{2} + 5e - 4$ |
| 53 | $[53, 53, w + 13]$ | $-5e^{3} + 8e^{2} + 5e - 3$ |
| 53 | $[53, 53, w + 39]$ | $-2e^{3} + 7e + 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |