Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[16, 4, 4]$ |
Dimension: | $5$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 3x^{4} - 5x^{3} - 19x^{2} - 10x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 6]$ | $\phantom{-}e$ |
3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $\phantom{-}0$ |
11 | $[11, 11, -3w - 17]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 12e$ |
11 | $[11, 11, 3w - 20]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 12e$ |
13 | $[13, 13, 2w - 13]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 13e - 3$ |
13 | $[13, 13, 2w + 11]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 13e - 3$ |
17 | $[17, 17, w + 7]$ | $-e^{4} - e^{3} + 7e^{2} + 6e - 2$ |
17 | $[17, 17, -w + 8]$ | $-e^{4} - e^{3} + 7e^{2} + 6e - 2$ |
19 | $[19, 19, -w - 4]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 11e - 1$ |
19 | $[19, 19, -w + 5]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 11e - 1$ |
25 | $[25, 5, 5]$ | $-e^{2} - e + 5$ |
31 | $[31, 31, -6w - 35]$ | $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 17e - 4$ |
31 | $[31, 31, -6w + 41]$ | $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 17e - 4$ |
37 | $[37, 37, -w - 1]$ | $\phantom{-}e^{4} - 8e^{2} + 6$ |
37 | $[37, 37, w - 2]$ | $\phantom{-}e^{4} - 8e^{2} + 6$ |
47 | $[47, 47, 3w + 16]$ | $\phantom{-}e^{3} + e^{2} - 8e - 8$ |
47 | $[47, 47, -3w + 19]$ | $\phantom{-}e^{3} + e^{2} - 8e - 8$ |
49 | $[49, 7, -7]$ | $-e^{4} - e^{3} + 6e^{2} + 9e + 10$ |
67 | $[67, 67, 3w - 22]$ | $\phantom{-}e^{4} - 8e^{2} + 4e + 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $1$ |