Base field \(\Q(\sqrt{145}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 36\); narrow class number \(4\) and class number \(4\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3,3,-w + 1]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 37x^{12} + 198x^{8} + 212x^{4} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{388}{1043}e^{15} + \frac{14367}{1043}e^{11} + \frac{77234}{1043}e^{7} + \frac{84451}{1043}e^{3}$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-\frac{753}{19817}e^{13} - \frac{28256}{19817}e^{9} - \frac{8587}{1043}e^{5} - \frac{193323}{19817}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{5345}{19817}e^{15} - \frac{197516}{19817}e^{11} - \frac{55242}{1043}e^{7} - \frac{1102322}{19817}e^{3}$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{3510}{19817}e^{14} - \frac{130448}{19817}e^{10} - \frac{37592}{1043}e^{6} - \frac{803799}{19817}e^{2}$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}\frac{23865}{19817}e^{15} + \frac{882023}{19817}e^{11} + \frac{246777}{1043}e^{7} + \frac{4869874}{19817}e^{3}$ |
| 17 | $[17, 17, w + 15]$ | $\phantom{-}\frac{641}{19817}e^{13} + \frac{21711}{19817}e^{9} + \frac{3099}{1043}e^{5} - \frac{64235}{19817}e$ |
| 29 | $[29, 29, w + 14]$ | $\phantom{-}\frac{1139}{2831}e^{14} + \frac{41966}{2831}e^{10} + \frac{11558}{149}e^{6} + \frac{226724}{2831}e^{2}$ |
| 37 | $[37, 37, w + 10]$ | $-\frac{1251}{19817}e^{13} - \frac{45680}{19817}e^{9} - \frac{11831}{1043}e^{5} - \frac{204013}{19817}e$ |
| 37 | $[37, 37, w + 26]$ | $\phantom{-}\frac{27750}{19817}e^{15} + \frac{1026069}{19817}e^{11} + \frac{287993}{1043}e^{7} + \frac{5815189}{19817}e^{3}$ |
| 43 | $[43, 43, w + 19]$ | $-\frac{1723}{19817}e^{13} - \frac{60523}{19817}e^{9} - \frac{12162}{1043}e^{5} - \frac{1331}{19817}e$ |
| 43 | $[43, 43, w + 23]$ | $-\frac{15242}{19817}e^{15} - \frac{563370}{19817}e^{11} - \frac{157712}{1043}e^{7} - \frac{3120743}{19817}e^{3}$ |
| 47 | $[47, 47, w + 22]$ | $\phantom{-}\frac{43433}{19817}e^{15} + \frac{1606540}{19817}e^{11} + \frac{451669}{1043}e^{7} + \frac{9105367}{19817}e^{3}$ |
| 47 | $[47, 47, w + 24]$ | $-\frac{1122}{19817}e^{13} - \frac{39734}{19817}e^{9} - \frac{8490}{1043}e^{5} - \frac{117917}{19817}e$ |
| 49 | $[49, 7, -7]$ | $-\frac{116}{1043}e^{12} - \frac{4134}{1043}e^{8} - \frac{17553}{1043}e^{4} - \frac{12786}{1043}$ |
| 59 | $[59, 59, w + 16]$ | $-\frac{9024}{19817}e^{14} - \frac{334832}{19817}e^{10} - \frac{95602}{1043}e^{6} - \frac{1905849}{19817}e^{2}$ |
| 59 | $[59, 59, w + 42]$ | $\phantom{-}\frac{8629}{19817}e^{14} + \frac{320773}{19817}e^{10} + \frac{92786}{1043}e^{6} + \frac{2084955}{19817}e^{2}$ |
| 71 | $[71, 71, w + 21]$ | $-\frac{12133}{19817}e^{14} - \frac{449101}{19817}e^{10} - \frac{126657}{1043}e^{6} - \frac{2533113}{19817}e^{2}$ |
| 71 | $[71, 71, w + 49]$ | $-\frac{15159}{19817}e^{14} - \frac{560466}{19817}e^{10} - \frac{157519}{1043}e^{6} - \frac{3303920}{19817}e^{2}$ |
| 73 | $[73, 73, w + 13]$ | $\phantom{-}\frac{7043}{19817}e^{15} + \frac{262417}{19817}e^{11} + \frac{76758}{1043}e^{7} + \frac{1712509}{19817}e^{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 1]$ | $\frac{5345}{19817}e^{15} + \frac{197516}{19817}e^{11} + \frac{55242}{1043}e^{7} + \frac{1102322}{19817}e^{3}$ |