Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[13,13,-w + 4]$ |
| Dimension: | $31$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $124$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{31} + 6x^{30} - 46x^{29} - 335x^{28} + 796x^{27} + 8128x^{26} - 4834x^{25} - 112214x^{24} - 36144x^{23} + 968341x^{22} + 884430x^{21} - 5387563x^{20} - 7427341x^{19} + 19103025x^{18} + 35386684x^{17} - 40186546x^{16} - 103268848x^{15} + 37927366x^{14} + 183040502x^{13} + 19239890x^{12} - 184723348x^{11} - 79857451x^{10} + 91070301x^{9} + 67204723x^{8} - 12309723x^{7} - 20754331x^{6} - 3486295x^{5} + 1440687x^{4} + 478923x^{3} - 1107x^{2} - 13624x - 1216\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, -w + 8]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $...$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w]$ | $...$ |
| 17 | $[17, 17, w + 16]$ | $...$ |
| 31 | $[31, 31, -w - 4]$ | $...$ |
| 31 | $[31, 31, w - 5]$ | $...$ |
| 41 | $[41, 41, 3w - 22]$ | $...$ |
| 47 | $[47, 47, w + 19]$ | $...$ |
| 47 | $[47, 47, w + 27]$ | $...$ |
| 53 | $[53, 53, w + 14]$ | $...$ |
| 53 | $[53, 53, w + 38]$ | $...$ |
| 59 | $[59, 59, -w - 10]$ | $...$ |
| 59 | $[59, 59, w - 11]$ | $...$ |
| 61 | $[61, 61, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,-w + 4]$ | $-1$ |