Base field 3.3.148.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[37, 37, w - 4]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w^{2} + w + 1]$ | $\phantom{-}e$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $-2e + 2$ |
17 | $[17, 17, 2w + 1]$ | $-2e + 3$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}2e - 1$ |
23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}2e$ |
25 | $[25, 5, -2w^{2} + w + 4]$ | $-2e + 2$ |
27 | $[27, 3, 3]$ | $-2e - 2$ |
29 | $[29, 29, w^{2} - 3w - 1]$ | $\phantom{-}2e - 6$ |
31 | $[31, 31, 2w^{2} - 2w - 3]$ | $-3e + 2$ |
37 | $[37, 37, w^{2} + w - 5]$ | $-1$ |
37 | $[37, 37, w - 4]$ | $\phantom{-}1$ |
43 | $[43, 43, 2w^{2} - w - 2]$ | $-2e + 8$ |
59 | $[59, 59, 2w^{2} - 3w - 6]$ | $-2e + 6$ |
61 | $[61, 61, -3w^{2} + 4w + 4]$ | $\phantom{-}e - 10$ |
67 | $[67, 67, -w - 4]$ | $\phantom{-}3e - 4$ |
67 | $[67, 67, -3w^{2} + 8]$ | $\phantom{-}2e + 8$ |
67 | $[67, 67, w^{2} - 3w - 3]$ | $-4e - 7$ |
79 | $[79, 79, w^{2} + 2w - 4]$ | $\phantom{-}6e + 2$ |
89 | $[89, 89, 3w^{2} - 3w - 5]$ | $-4e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$37$ | $[37, 37, w - 4]$ | $-1$ |