Base field 4.4.4205.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[35, 35, -w^{3} + 3w^{2} + w - 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + 2x^{2} - 16x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{3} + w^{2} + 5w]$ | $\phantom{-}1$ |
7 | $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w]$ | $\phantom{-}1$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{2} - e + 6$ |
13 | $[13, 13, -w^{2} + w + 2]$ | $\phantom{-}2$ |
16 | $[16, 2, 2]$ | $\phantom{-}e + 3$ |
23 | $[23, 23, -w^{2} + 3w + 1]$ | $-\frac{1}{2}e^{2} - e + 4$ |
23 | $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ | $\phantom{-}0$ |
25 | $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 6$ |
49 | $[49, 7, w^{3} - w^{2} - 6w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - 6$ |
53 | $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ | $-e + 2$ |
53 | $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ | $-6$ |
67 | $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ | $-e^{2} + 12$ |
67 | $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ | $-2e$ |
81 | $[81, 3, -3]$ | $-\frac{1}{2}e^{2} - e + 2$ |
83 | $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ | $\phantom{-}\frac{3}{2}e^{2} + 3e - 12$ |
83 | $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ | $-e^{2} - 2e + 8$ |
103 | $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ | $-\frac{1}{2}e^{2} + 2e + 12$ |
103 | $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ | $\phantom{-}e^{2} - 2e - 16$ |
107 | $[107, 107, w^{3} - w^{2} - 3w - 3]$ | $-\frac{1}{2}e^{2} - 4e + 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -w^{3} + w^{2} + 5w]$ | $-1$ |
$7$ | $[7, 7, w^{3} - 2w^{2} - 3w]$ | $-1$ |