Base field \(\Q(\sqrt{97}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 24\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[6, 6, 5w + 22]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 6x^{2} - 7x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, 7w - 38]$ | $\phantom{-}1$ |
2 | $[2, 2, -7w - 31]$ | $\phantom{-}e$ |
3 | $[3, 3, 2w + 9]$ | $\phantom{-}e^{3} - e^{2} - 5e + 1$ |
3 | $[3, 3, 2w - 11]$ | $\phantom{-}1$ |
11 | $[11, 11, -12w + 65]$ | $-2e^{3} + 10e + 2$ |
11 | $[11, 11, -12w - 53]$ | $\phantom{-}e^{3} - e^{2} - 3e + 3$ |
25 | $[25, 5, 5]$ | $-2e - 2$ |
31 | $[31, 31, 8w - 43]$ | $-e^{3} + e^{2} + 5e + 1$ |
31 | $[31, 31, 8w + 35]$ | $-3e^{3} - e^{2} + 15e + 9$ |
43 | $[43, 43, 54w + 239]$ | $\phantom{-}2e^{2} - 2e - 2$ |
43 | $[43, 43, -54w + 293]$ | $\phantom{-}4e - 2$ |
47 | $[47, 47, 2w - 13]$ | $\phantom{-}2e^{3} - 10e - 10$ |
47 | $[47, 47, -2w - 11]$ | $-2e^{3} + 10e + 4$ |
49 | $[49, 7, -7]$ | $-3e^{3} + e^{2} + 17e + 3$ |
53 | $[53, 53, 4w + 19]$ | $-2e^{2} - 2e + 10$ |
53 | $[53, 53, 4w - 23]$ | $\phantom{-}e^{3} - 3e^{2} - 7e + 7$ |
61 | $[61, 61, 2w - 7]$ | $-2e^{3} + 4e^{2} + 8e - 12$ |
61 | $[61, 61, -2w - 5]$ | $\phantom{-}3e^{3} + e^{2} - 17e - 11$ |
73 | $[73, 73, 22w + 97]$ | $\phantom{-}6$ |
73 | $[73, 73, -22w + 119]$ | $\phantom{-}2e^{3} - 14e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, 7w - 38]$ | $-1$ |
$3$ | $[3, 3, 2w - 11]$ | $-1$ |