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: | $[10, 10, -9w + 80]$ |
Dimension: | $17$ |
CM: | no |
Base change: | no |
Newspace dimension: | $53$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{17} - x^{16} - 27x^{15} + 22x^{14} + 298x^{13} - 180x^{12} - 1733x^{11} + 651x^{10} + 5668x^{9} - 805x^{8} - 10164x^{7} - 823x^{6} + 8699x^{5} + 2350x^{4} - 2228x^{3} - 780x^{2} + 22x + 6\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 8]$ | $\phantom{-}1$ |
2 | $[2, 2, -w + 9]$ | $\phantom{-}e$ |
5 | $[5, 5, -76w + 675]$ | $\phantom{-}1$ |
5 | $[5, 5, 76w + 599]$ | $...$ |
7 | $[7, 7, -8w - 63]$ | $...$ |
7 | $[7, 7, -8w + 71]$ | $...$ |
9 | $[9, 3, 3]$ | $...$ |
17 | $[17, 17, 42w + 331]$ | $...$ |
17 | $[17, 17, 42w - 373]$ | $...$ |
29 | $[29, 29, -6w - 47]$ | $...$ |
29 | $[29, 29, 6w - 53]$ | $...$ |
31 | $[31, 31, 10w + 79]$ | $...$ |
31 | $[31, 31, -10w + 89]$ | $...$ |
43 | $[43, 43, 2w - 19]$ | $...$ |
43 | $[43, 43, -2w - 17]$ | $...$ |
53 | $[53, 53, 194w + 1529]$ | $...$ |
53 | $[53, 53, -194w + 1723]$ | $...$ |
59 | $[59, 59, -110w - 867]$ | $...$ |
59 | $[59, 59, 110w - 977]$ | $...$ |
79 | $[79, 79, 650w - 5773]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w + 8]$ | $-1$ |
$5$ | $[5, 5, -76w + 675]$ | $-1$ |