Base field \(\Q(\sqrt{67}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, 16w + 131]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 30x^{16} + 378x^{14} - 2608x^{12} + 10771x^{10} - 27344x^{8} + 42180x^{6} - 37713x^{4} + 17698x^{2} - 3332\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -27w + 221]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 8]$ | $\phantom{-}\frac{3267}{9478}e^{17} - \frac{44987}{4739}e^{15} + \frac{72576}{677}e^{13} - \frac{3042574}{4739}e^{11} + \frac{20893191}{9478}e^{9} - \frac{20779666}{4739}e^{7} + \frac{23076279}{4739}e^{5} - \frac{25987919}{9478}e^{3} + \frac{2846716}{4739}e$ |
| 3 | $[3, 3, -w - 8]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -11w + 90]$ | $\phantom{-}\frac{751}{4739}e^{17} - \frac{19457}{4739}e^{15} + \frac{28790}{677}e^{13} - \frac{1062685}{4739}e^{11} + \frac{2993567}{4739}e^{9} - \frac{4265419}{4739}e^{7} + \frac{2457668}{4739}e^{5} - \frac{79787}{4739}e^{3} - \frac{231654}{4739}e$ |
| 7 | $[7, 7, -11w - 90]$ | $\phantom{-}\frac{6515}{9478}e^{17} - \frac{89283}{4739}e^{15} + \frac{143057}{677}e^{13} - \frac{5938215}{4739}e^{11} + \frac{40188411}{9478}e^{9} - \frac{39126981}{4739}e^{7} + \frac{42161394}{4739}e^{5} - \frac{45680907}{9478}e^{3} + \frac{4757870}{4739}e$ |
| 11 | $[11, 11, 6w - 49]$ | $-\frac{1199}{9478}e^{17} + \frac{15920}{4739}e^{15} - \frac{24420}{677}e^{13} + \frac{952557}{4739}e^{11} - \frac{5881795}{9478}e^{9} + \frac{4986361}{4739}e^{7} - \frac{4386639}{4739}e^{5} + \frac{3774583}{9478}e^{3} - \frac{339138}{4739}e$ |
| 11 | $[11, 11, 6w + 49]$ | $-\frac{1024}{4739}e^{17} + \frac{30335}{4739}e^{15} - \frac{53469}{677}e^{13} + \frac{2493555}{4739}e^{11} - \frac{9709094}{4739}e^{9} + \frac{22278190}{4739}e^{7} - \frac{28734597}{4739}e^{5} + \frac{18427613}{4739}e^{3} - \frac{4447986}{4739}e$ |
| 17 | $[17, 17, 4w + 33]$ | $\phantom{-}\frac{16}{677}e^{16} - \frac{273}{677}e^{14} + \frac{612}{677}e^{12} + \frac{15780}{677}e^{10} - \frac{141923}{677}e^{8} + \frac{508541}{677}e^{6} - \frac{876937}{677}e^{4} + \frac{689244}{677}e^{2} - \frac{193959}{677}$ |
| 17 | $[17, 17, -4w + 33]$ | $-\frac{103}{677}e^{16} + \frac{2646}{677}e^{14} - \frac{27127}{677}e^{12} + \frac{141290}{677}e^{10} - \frac{392346}{677}e^{8} + \frac{551275}{677}e^{6} - \frac{319215}{677}e^{4} + \frac{23914}{677}e^{2} + \frac{24045}{677}$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{81}{677}e^{16} - \frac{2186}{677}e^{14} + \frac{23916}{677}e^{12} - \frac{136246}{677}e^{10} + \frac{432034}{677}e^{8} - \frac{757409}{677}e^{6} + \frac{693732}{677}e^{4} - \frac{305118}{677}e^{2} + \frac{50296}{677}$ |
| 29 | $[29, 29, -70w + 573]$ | $-\frac{941}{677}e^{16} + \frac{25830}{677}e^{14} - \frac{290376}{677}e^{12} + \frac{1727979}{677}e^{10} - \frac{5878743}{677}e^{8} + \frac{11539615}{677}e^{6} - \frac{12580413}{677}e^{4} + \frac{6921368}{677}e^{2} - \frac{1469961}{677}$ |
| 29 | $[29, 29, 151w - 1236]$ | $-\frac{265}{677}e^{16} + \frac{7018}{677}e^{14} - \frac{74959}{677}e^{12} + \frac{413782}{677}e^{10} - \frac{1256414}{677}e^{8} + \frac{2066093}{677}e^{6} - \frac{1706679}{677}e^{4} + \frac{634150}{677}e^{2} - \frac{76547}{677}$ |
| 31 | $[31, 31, -w - 6]$ | $\phantom{-}\frac{3697}{9478}e^{17} - \frac{46159}{4739}e^{15} + \frac{64297}{677}e^{13} - \frac{2124250}{4739}e^{11} + \frac{9326091}{9478}e^{9} - \frac{2395807}{4739}e^{7} - \frac{6711573}{4739}e^{5} + \frac{18211077}{9478}e^{3} - \frac{2988348}{4739}e$ |
| 31 | $[31, 31, w - 6]$ | $-\frac{48}{677}e^{17} + \frac{819}{677}e^{15} - \frac{1836}{677}e^{13} - \frac{47340}{677}e^{11} + \frac{425092}{677}e^{9} - \frac{1513437}{677}e^{7} + \frac{2557695}{677}e^{5} - \frac{1906606}{677}e^{3} + \frac{491836}{677}e$ |
| 37 | $[37, 37, -21w - 172]$ | $\phantom{-}\frac{448}{677}e^{16} - \frac{11706}{677}e^{14} + \frac{122748}{677}e^{12} - \frac{659639}{677}e^{10} + \frac{1919441}{677}e^{8} - \frac{2924833}{677}e^{6} + \frac{2059311}{677}e^{4} - \frac{522374}{677}e^{2} + \frac{6135}{677}$ |
| 37 | $[37, 37, -21w + 172]$ | $-\frac{1061}{677}e^{16} + \frac{28893}{677}e^{14} - \frac{321369}{677}e^{12} + \frac{1885168}{677}e^{10} - \frac{6291196}{677}e^{8} + \frac{12043802}{677}e^{6} - \frac{12749352}{677}e^{4} + \frac{6840370}{677}e^{2} - \frac{1431891}{677}$ |
| 43 | $[43, 43, 2w - 15]$ | $-\frac{6788}{4739}e^{17} + \frac{184705}{4739}e^{15} - \frac{293191}{677}e^{13} + \frac{12023031}{4739}e^{11} - \frac{40051344}{4739}e^{9} + \frac{76486147}{4739}e^{7} - \frac{80701366}{4739}e^{5} + \frac{43129743}{4739}e^{3} - \frac{8973002}{4739}e$ |
| 43 | $[43, 43, 2w + 15]$ | $\phantom{-}\frac{1808}{4739}e^{17} - \frac{48451}{4739}e^{15} + \frac{75355}{677}e^{13} - \frac{3004604}{4739}e^{11} + \frac{9616939}{4739}e^{9} - \frac{17310871}{4739}e^{7} + \frac{16686659}{4739}e^{5} - \frac{7790455}{4739}e^{3} + \frac{1317950}{4739}e$ |
| 67 | $[67, 67, -w]$ | $\phantom{-}\frac{13859}{9478}e^{17} - \frac{189510}{4739}e^{15} + \frac{302874}{677}e^{13} - \frac{12536697}{4739}e^{11} + \frac{84614819}{9478}e^{9} - \frac{82250090}{4739}e^{7} + \frac{88817352}{4739}e^{5} - \frac{97295845}{9478}e^{3} + \frac{10371052}{4739}e$ |
| 73 | $[73, 73, -3w - 26]$ | $\phantom{-}\frac{592}{677}e^{16} - \frac{16194}{677}e^{14} + \frac{181062}{677}e^{12} - \frac{1068020}{677}e^{10} + \frac{3580991}{677}e^{8} - \frac{6861239}{677}e^{6} + \frac{7191681}{677}e^{4} - \frac{3730832}{677}e^{2} + \frac{733585}{677}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 8]$ | $1$ |