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: | $[9, 3, 3]$ |
Dimension: | $30$ |
CM: | no |
Base change: | no |
Newspace dimension: | $100$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{30} - 3x^{29} - 42x^{28} + 131x^{27} + 767x^{26} - 2523x^{25} - 7955x^{24} + 28219x^{23} + 51106x^{22} - 202994x^{21} - 205513x^{20} + 981779x^{19} + 475961x^{18} - 3237610x^{17} - 361044x^{16} + 7215057x^{15} - 1196333x^{14} - 10507920x^{13} + 3991896x^{12} + 9336804x^{11} - 5149526x^{10} - 4439546x^{9} + 3101669x^{8} + 889388x^{7} - 755535x^{6} - 80815x^{5} + 70140x^{4} + 6198x^{3} - 1685x^{2} - 229x - 7\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 8]$ | $...$ |
2 | $[2, 2, -w + 9]$ | $\phantom{-}e$ |
5 | $[5, 5, -76w + 675]$ | $...$ |
5 | $[5, 5, 76w + 599]$ | $...$ |
7 | $[7, 7, -8w - 63]$ | $...$ |
7 | $[7, 7, -8w + 71]$ | $...$ |
9 | $[9, 3, 3]$ | $-1$ |
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 |
---|---|---|
$9$ | $[9, 3, 3]$ | $1$ |