Base field \(\Q(\sqrt{17}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[144,48,-3w + 15]$ |
Dimension: | $3$ |
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:
\(x^{3} - 7x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
2 | $[2, 2, -w - 1]$ | $\phantom{-}0$ |
9 | $[9, 3, 3]$ | $-1$ |
13 | $[13, 13, -2w + 3]$ | $\phantom{-}e^{2} - 2e - 5$ |
13 | $[13, 13, 2w + 1]$ | $-e^{2} + 3$ |
17 | $[17, 17, -2w + 1]$ | $\phantom{-}2e$ |
19 | $[19, 19, -2w + 7]$ | $-e^{2} + 5$ |
19 | $[19, 19, 2w + 5]$ | $\phantom{-}e^{2} - 2e - 3$ |
25 | $[25, 5, -5]$ | $-e^{2} - 2e + 5$ |
43 | $[43, 43, 4w - 7]$ | $-e^{2} - 2e + 7$ |
43 | $[43, 43, 4w + 3]$ | $-e^{2} + 2e + 3$ |
47 | $[47, 47, -2w + 9]$ | $-2e + 2$ |
47 | $[47, 47, 2w + 7]$ | $-2e^{2} + 10$ |
49 | $[49, 7, -7]$ | $-2e^{2} + 2e + 6$ |
53 | $[53, 53, 4w - 13]$ | $\phantom{-}6$ |
53 | $[53, 53, 6w - 13]$ | $\phantom{-}2e^{2} - 2e - 10$ |
59 | $[59, 59, -4w - 1]$ | $\phantom{-}4$ |
59 | $[59, 59, 4w - 5]$ | $\phantom{-}4$ |
67 | $[67, 67, 4w - 3]$ | $\phantom{-}2e^{2} + 2e - 8$ |
67 | $[67, 67, 4w - 1]$ | $\phantom{-}4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,w + 1]$ | $1$ |
$9$ | $[9,3,3]$ | $1$ |