Base field \(\Q(\sqrt{3}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[37, 37, 2 w - 7]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 5 x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-e^{3} + 4 e$ |
| 11 | $[11, 11, -2 w + 1]$ | $\phantom{-}e^{3} - 5 e$ |
| 11 | $[11, 11, 2 w + 1]$ | $\phantom{-}e^{3} - 5 e$ |
| 13 | $[13, 13, w + 4]$ | $-e^{2} + 4$ |
| 13 | $[13, 13, -w + 4]$ | $\phantom{-}2 e^{2} - 4$ |
| 23 | $[23, 23, -3 w + 2]$ | $-2 e^{3} + 7 e$ |
| 23 | $[23, 23, 3 w + 2]$ | $\phantom{-}2 e^{3} - 10 e$ |
| 25 | $[25, 5, 5]$ | $-2 e^{2} + 6$ |
| 37 | $[37, 37, 2 w - 7]$ | $-1$ |
| 37 | $[37, 37, -2 w - 7]$ | $-3 e^{2} + 8$ |
| 47 | $[47, 47, -4 w - 1]$ | $-2 e^{3} + 15 e$ |
| 47 | $[47, 47, 4 w - 1]$ | $\phantom{-}3 e^{3} - 11 e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}5 e^{2} - 14$ |
| 59 | $[59, 59, 5 w - 4]$ | $-7 e^{3} + 26 e$ |
| 59 | $[59, 59, -5 w - 4]$ | $\phantom{-}3 e^{3} - 7 e$ |
| 61 | $[61, 61, -w - 8]$ | $\phantom{-}e^{2} - 4$ |
| 61 | $[61, 61, w - 8]$ | $-2 e^{2} + 4$ |
| 71 | $[71, 71, 5 w - 2]$ | $\phantom{-}5 e$ |
| 71 | $[71, 71, -5 w - 2]$ | $\phantom{-}2 e^{3} - 13 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, 2 w - 7]$ | $1$ |