Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 10x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 8]$ | $-1$ |
2 | $[2, 2, -w + 9]$ | $\phantom{-}1$ |
5 | $[5, 5, -76w + 675]$ | $\phantom{-}e$ |
5 | $[5, 5, 76w + 599]$ | $-2e^{2} - 5e + 12$ |
7 | $[7, 7, -8w - 63]$ | $-1$ |
7 | $[7, 7, -8w + 71]$ | $\phantom{-}2e^{2} + 4e - 13$ |
9 | $[9, 3, 3]$ | $\phantom{-}2e^{2} + 5e - 14$ |
17 | $[17, 17, 42w + 331]$ | $-4e^{2} - 9e + 24$ |
17 | $[17, 17, 42w - 373]$ | $-e$ |
29 | $[29, 29, -6w - 47]$ | $-e^{2} - e + 12$ |
29 | $[29, 29, 6w - 53]$ | $\phantom{-}e^{2} + e - 6$ |
31 | $[31, 31, 10w + 79]$ | $-e^{2} - e + 5$ |
31 | $[31, 31, -10w + 89]$ | $\phantom{-}5e^{2} + 13e - 31$ |
43 | $[43, 43, 2w - 19]$ | $\phantom{-}5e^{2} + 12e - 31$ |
43 | $[43, 43, -2w - 17]$ | $\phantom{-}e^{2} - 13$ |
53 | $[53, 53, 194w + 1529]$ | $-8e^{2} - 19e + 48$ |
53 | $[53, 53, -194w + 1723]$ | $-6e^{2} - 17e + 36$ |
59 | $[59, 59, -110w - 867]$ | $-3e$ |
59 | $[59, 59, 110w - 977]$ | $-e - 6$ |
79 | $[79, 79, 650w - 5773]$ | $\phantom{-}9e^{2} + 23e - 55$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w + 8]$ | $1$ |
$2$ | $[2, 2, -w + 9]$ | $-1$ |