Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 9x^{9} + 11x^{8} - 100x^{7} - 239x^{6} + 326x^{5} + 1032x^{4} - 378x^{3} - 1456x^{2} + 220x + 573\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}\frac{3677}{61921}e^{9} + \frac{12870}{61921}e^{8} - \frac{67115}{61921}e^{7} - \frac{210206}{61921}e^{6} + \frac{459949}{61921}e^{5} + \frac{1152840}{61921}e^{4} - \frac{1331309}{61921}e^{3} - \frac{2355248}{61921}e^{2} + \frac{1211831}{61921}e + \frac{1248446}{61921}$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-\frac{9726}{61921}e^{9} - \frac{49030}{61921}e^{8} + \frac{98259}{61921}e^{7} + \frac{660271}{61921}e^{6} - \frac{278210}{61921}e^{5} - \frac{2903919}{61921}e^{4} + \frac{348677}{61921}e^{3} + \frac{4724527}{61921}e^{2} - \frac{395517}{61921}e - \frac{2224050}{61921}$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}\frac{4358}{61921}e^{9} + \frac{16685}{61921}e^{8} - \frac{76497}{61921}e^{7} - \frac{281706}{61921}e^{6} + \frac{481950}{61921}e^{5} + \frac{1592144}{61921}e^{4} - \frac{1197979}{61921}e^{3} - \frac{3347950}{61921}e^{2} + \frac{816907}{61921}e + \frac{1964592}{61921}$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $-\frac{1263}{61921}e^{9} + \frac{17202}{61921}e^{8} + \frac{158700}{61921}e^{7} + \frac{15856}{61921}e^{6} - \frac{1688666}{61921}e^{5} - \frac{1560797}{61921}e^{4} + \frac{5279513}{61921}e^{3} + \frac{5363768}{61921}e^{2} - \frac{4117042}{61921}e - \frac{3402127}{61921}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $-\frac{4508}{61921}e^{9} - \frac{5523}{61921}e^{8} + \frac{160943}{61921}e^{7} + \frac{296091}{61921}e^{6} - \frac{1410701}{61921}e^{5} - \frac{2633816}{61921}e^{4} + \frac{4180645}{61921}e^{3} + \frac{6794955}{61921}e^{2} - \frac{3531640}{61921}e - \frac{3907404}{61921}$ |
| 23 | $[23, 23, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{14054}{61921}e^{9} + \frac{105100}{61921}e^{8} + \frac{77433}{61921}e^{7} - \frac{1001021}{61921}e^{6} - \frac{2013888}{61921}e^{5} + \frac{1835657}{61921}e^{4} + \frac{6839539}{61921}e^{3} + \frac{2276600}{61921}e^{2} - \frac{4866260}{61921}e - \frac{3357988}{61921}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}\frac{5388}{61921}e^{9} - \frac{14552}{61921}e^{8} - \frac{313730}{61921}e^{7} - \frac{256641}{61921}e^{6} + \frac{3049168}{61921}e^{5} + \frac{3828431}{61921}e^{4} - \frac{9220447}{61921}e^{3} - \frac{11392652}{61921}e^{2} + \frac{7284405}{61921}e + \frac{6983052}{61921}$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{13892}{61921}e^{9} + \frac{70095}{61921}e^{8} - \frac{145924}{61921}e^{7} - \frac{973101}{61921}e^{6} + \frac{418438}{61921}e^{5} + \frac{4398666}{61921}e^{4} - \frac{384016}{61921}e^{3} - \frac{7152655}{61921}e^{2} + \frac{303572}{61921}e + \frac{2950170}{61921}$ |
| 29 | $[29, 29, -w + 3]$ | $\phantom{-}\frac{22413}{61921}e^{9} + \frac{80823}{61921}e^{8} - \frac{424438}{61921}e^{7} - \frac{1424931}{61921}e^{6} + \frac{2856141}{61921}e^{5} + \frac{8247405}{61921}e^{4} - \frac{7682906}{61921}e^{3} - \frac{17138534}{61921}e^{2} + \frac{6080245}{61921}e + \frac{9220689}{61921}$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}\frac{8185}{61921}e^{9} + \frac{18393}{61921}e^{8} - \frac{228058}{61921}e^{7} - \frac{506297}{61921}e^{6} + \frac{1870650}{61921}e^{5} + \frac{3786656}{61921}e^{4} - \frac{5511954}{61921}e^{3} - \frac{9150203}{61921}e^{2} + \frac{4619629}{61921}e + \frac{4908166}{61921}$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $-\frac{19161}{61921}e^{9} - \frac{77608}{61921}e^{8} + \frac{307622}{61921}e^{7} + \frac{1224522}{61921}e^{6} - \frac{1859362}{61921}e^{5} - \frac{6454551}{61921}e^{4} + \frac{4957045}{61921}e^{3} + \frac{12526806}{61921}e^{2} - \frac{4293704}{61921}e - \frac{6417883}{61921}$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $\phantom{-}\frac{3635}{61921}e^{9} + \frac{6088}{61921}e^{8} - \frac{122729}{61921}e^{7} - \frac{255715}{61921}e^{6} + \frac{1046978}{61921}e^{5} + \frac{2159036}{61921}e^{4} - \frac{2965572}{61921}e^{3} - \frac{5439720}{61921}e^{2} + \frac{2026976}{61921}e + \frac{3253127}{61921}$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $\phantom{-}\frac{13527}{61921}e^{9} + \frac{105512}{61921}e^{8} + \frac{104970}{61921}e^{7} - \frac{969058}{61921}e^{6} - \frac{2289418}{61921}e^{5} + \frac{1504789}{61921}e^{4} + \frac{7703546}{61921}e^{3} + \frac{2958525}{61921}e^{2} - \frac{5478729}{61921}e - \frac{3498743}{61921}$ |
| 59 | $[59, 59, w^{2} + w - 4]$ | $\phantom{-}\frac{32407}{61921}e^{9} + \frac{170180}{61921}e^{8} - \frac{273977}{61921}e^{7} - \frac{2160440}{61921}e^{6} + \frac{332105}{61921}e^{5} + \frac{8502119}{61921}e^{4} + \frac{603811}{61921}e^{3} - \frac{11121405}{61921}e^{2} + \frac{195166}{61921}e + \frac{3482803}{61921}$ |
| 61 | $[61, 61, -2w^{2} + w + 8]$ | $\phantom{-}\frac{11554}{61921}e^{9} + \frac{84730}{61921}e^{8} + \frac{40043}{61921}e^{7} - \frac{885113}{61921}e^{6} - \frac{1434892}{61921}e^{5} + \frac{2369626}{61921}e^{4} + \frac{5218130}{61921}e^{3} - \frac{914616}{61921}e^{2} - \frac{4414112}{61921}e - \frac{814744}{61921}$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $-\frac{22166}{61921}e^{9} - \frac{105808}{61921}e^{8} + \frac{273825}{61921}e^{7} + \frac{1543662}{61921}e^{6} - \frac{1185205}{61921}e^{5} - \frac{7545146}{61921}e^{4} + \frac{2590640}{61921}e^{3} + \frac{13953754}{61921}e^{2} - \frac{2634158}{61921}e - \frac{7418463}{61921}$ |
| 79 | $[79, 79, 2w^{2} + w - 6]$ | $-\frac{4269}{61921}e^{9} + \frac{635}{61921}e^{8} + \frac{176654}{61921}e^{7} + \frac{217442}{61921}e^{6} - \frac{1585833}{61921}e^{5} - \frac{2232320}{61921}e^{4} + \frac{4503309}{61921}e^{3} + \frac{5697054}{61921}e^{2} - \frac{3044029}{61921}e - \frac{3023675}{61921}$ |
| 79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $-\frac{2628}{3259}e^{9} - \frac{17450}{3259}e^{8} + \frac{299}{3259}e^{7} + \frac{187497}{3259}e^{6} + \frac{216476}{3259}e^{5} - \frac{530389}{3259}e^{4} - \frac{801776}{3259}e^{3} + \frac{271451}{3259}e^{2} + \frac{567572}{3259}e + \frac{97873}{3259}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $-1$ |