Base field 4.4.13676.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[4, 2, -w^{2} - w + 3]$ |
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:
\(x^{4} - x^{3} - 6x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{2} - w + 3]$ | $-1$ |
5 | $[5, 5, w^{3} - 5w + 1]$ | $\phantom{-}e^{3} - e^{2} - 5e + 3$ |
11 | $[11, 11, -w^{3} + 6w - 2]$ | $-e^{3} + 6e + 1$ |
13 | $[13, 13, -w^{2} + 4]$ | $\phantom{-}e^{3} - e^{2} - 5e + 1$ |
17 | $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ | $-e^{2} + e + 4$ |
37 | $[37, 37, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}e^{3} - e^{2} - 7e + 1$ |
37 | $[37, 37, -w^{3} + 6w - 4]$ | $-e^{3} + e^{2} + 7e - 5$ |
41 | $[41, 41, -w^{3} + 5w - 5]$ | $-2e^{3} + e^{2} + 13e - 2$ |
43 | $[43, 43, w^{3} - 4w + 4]$ | $\phantom{-}2e^{3} - 2e^{2} - 8e + 2$ |
43 | $[43, 43, -2w^{3} + 11w - 2]$ | $-3e^{3} + 2e^{2} + 18e - 7$ |
47 | $[47, 47, -2w^{3} - w^{2} + 12w]$ | $-2$ |
47 | $[47, 47, 2w - 1]$ | $-2e + 4$ |
61 | $[61, 61, -w^{3} + w^{2} + 6w - 5]$ | $-2e^{3} + 2e^{2} + 10e - 2$ |
71 | $[71, 71, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}4e^{3} - 4e^{2} - 26e + 8$ |
71 | $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ | $-2e - 2$ |
79 | $[79, 79, w^{3} + w^{2} - 6w - 5]$ | $\phantom{-}2e^{3} - 2e^{2} - 12e$ |
81 | $[81, 3, -3]$ | $-3e^{3} + e^{2} + 17e + 3$ |
83 | $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ | $\phantom{-}4e + 2$ |
97 | $[97, 97, w^{3} + w^{2} - 6w + 1]$ | $\phantom{-}2e^{3} - 3e^{2} - 15e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{2} - w + 3]$ | $1$ |