Base field 4.4.11197.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 3x^{3} - 4x^{2} + 8x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $-1$ |
11 | $[11, 11, -w - 2]$ | $-e^{3} + 3e^{2} + 2e - 4$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ | $-e + 4$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $-e^{2} + 6$ |
16 | $[16, 2, 2]$ | $\phantom{-}e^{3} - 3e^{2} - 2e + 5$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $-e^{3} + 4e^{2} - 8$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}e^{3} - 4e^{2} + e + 8$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}e^{3} - 4e^{2} - 2e + 8$ |
27 | $[27, 3, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}4$ |
29 | $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ | $\phantom{-}e^{2} - 3e + 2$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $-e^{3} + 3e^{2} + 3e - 2$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ | $\phantom{-}e^{3} - e^{2} - 6e$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}e^{3} - 2e^{2} - 3e + 4$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $-e^{3} + 10e - 2$ |
67 | $[67, 67, -w^{3} + w^{2} + 5w - 1]$ | $-e^{3} + 2e^{2}$ |
67 | $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ | $-e^{3} + 2e^{2} + 8e - 8$ |
83 | $[83, 83, -2w + 3]$ | $-e^{3} - e^{2} + 10e + 4$ |
89 | $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ | $\phantom{-}3e^{2} - 9e - 6$ |
97 | $[97, 97, w^{3} - w^{2} - 4w - 3]$ | $\phantom{-}2e^{3} - 5e^{2} - 12e + 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $1$ |