Base field 4.4.11348.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[14, 14, w^{3} - 2w^{2} - 4w + 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 5x^{2} - 3x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $-1$ |
7 | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $-1$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $-e^{3} + 3e$ |
19 | $[19, 19, -2w + 1]$ | $-2e^{3} - e^{2} + 7e$ |
29 | $[29, 29, -w^{3} + w^{2} + 2w - 1]$ | $-e^{3} + 3e - 4$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ | $\phantom{-}e^{3} + e^{2} - 4e - 4$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 5]$ | $-e^{3} - e^{2} + 5e + 3$ |
43 | $[43, 43, -2w^{3} + 2w^{2} + 8w + 3]$ | $-4e^{2} + 14$ |
43 | $[43, 43, -w^{2} + 3w + 1]$ | $-2e^{3} + 10e - 2$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e^{3} + 5e^{2} - 14$ |
53 | $[53, 53, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}e^{2} - 2e - 3$ |
59 | $[59, 59, 2w^{3} - 2w^{2} - 10w + 3]$ | $\phantom{-}3e^{3} + 2e^{2} - 9e - 2$ |
61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $-3e^{2} - e + 6$ |
61 | $[61, 61, w^{2} + w - 3]$ | $-e^{3} + 4e^{2} + 8e - 13$ |
71 | $[71, 71, -w^{3} + 5w + 1]$ | $-4e^{3} - 3e^{2} + 12e + 5$ |
71 | $[71, 71, w^{3} - w^{2} - 4w - 3]$ | $-4e^{3} - e^{2} + 17e + 2$ |
81 | $[81, 3, -3]$ | $\phantom{-}2e^{3} - 6e + 8$ |
83 | $[83, 83, -3w^{3} + 5w^{2} + 12w - 9]$ | $\phantom{-}e^{3} + 5e^{2} - 3e - 9$ |
83 | $[83, 83, -3w^{3} + 6w^{2} + 13w - 13]$ | $-e^{3} - 6e^{2} + 2e + 15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w + 1]$ | $1$ |
$7$ | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $1$ |