Base field 4.4.3981.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 4x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[45, 15, w^{3} - w^{2} - 5w + 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 12x^{3} + 7x^{2} + 31x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}1$ |
9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}1$ |
13 | $[13, 13, -w^{3} + w^{2} + 4w]$ | $-e^{3} + 7e + 2$ |
16 | $[16, 2, 2]$ | $-e^{2} + e + 5$ |
23 | $[23, 23, w^{2} - 2w - 2]$ | $\phantom{-}e^{3} - e^{2} - 7e + 4$ |
37 | $[37, 37, w^{3} - 4w + 1]$ | $\phantom{-}e^{4} - e^{3} - 9e^{2} + 7e + 10$ |
37 | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}e^{4} - e^{3} - 9e^{2} + 7e + 10$ |
41 | $[41, 41, w^{3} - 5w + 1]$ | $-2e + 2$ |
43 | $[43, 43, 2w^{3} - w^{2} - 7w]$ | $-e^{3} - 2e^{2} + 9e + 8$ |
53 | $[53, 53, 2w - 3]$ | $-e^{4} + e^{3} + 9e^{2} - 8e - 10$ |
59 | $[59, 59, -2w^{3} + w^{2} + 9w - 1]$ | $\phantom{-}e^{3} + 3e^{2} - 9e - 16$ |
67 | $[67, 67, -w - 3]$ | $-e^{4} + e^{3} + 9e^{2} - 5e - 8$ |
67 | $[67, 67, w^{3} + w^{2} - 5w - 4]$ | $-e^{4} + 9e^{2} - e - 8$ |
71 | $[71, 71, 2w^{3} - 3w^{2} - 7w + 5]$ | $-2e^{2} + 8$ |
73 | $[73, 73, w^{3} - 6w]$ | $-e^{4} + e^{3} + 11e^{2} - 9e - 18$ |
73 | $[73, 73, -w^{3} - w^{2} + 5w + 3]$ | $\phantom{-}e^{4} - 9e^{2} + e + 6$ |
79 | $[79, 79, w^{3} - 3w - 4]$ | $\phantom{-}e^{4} - e^{3} - 9e^{2} + 5e + 12$ |
83 | $[83, 83, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}2e^{3} + 2e^{2} - 16e - 12$ |
83 | $[83, 83, -2w^{3} + 2w^{2} + 6w - 3]$ | $-e^{3} + e^{2} + 9e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w^{3} - w^{2} - 3w + 1]$ | $-1$ |
$9$ | $[9, 3, -w^{2} + 2]$ | $-1$ |