Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[25, 25, -w^{3} + w^{2} + 3w - 2]$ |
| Dimension: | $12$ |
| 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:
| \(x^{12} - 109x^{10} + 4152x^{8} - 63826x^{6} + 335379x^{4} - 383416x^{2} + 81729\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{97654596}{10362591478871}e^{10} - \frac{11342872158}{10362591478871}e^{8} + \frac{449017303235}{10362591478871}e^{6} - \frac{6721999934834}{10362591478871}e^{4} + \frac{26446785650130}{10362591478871}e^{2} + \frac{4289555351895}{10362591478871}$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $\phantom{-}\frac{206428944}{10362591478871}e^{10} - \frac{21293058316}{10362591478871}e^{8} + \frac{776454023793}{10362591478871}e^{6} - \frac{11674397286783}{10362591478871}e^{4} + \frac{60049894780119}{10362591478871}e^{2} - \frac{21181755960124}{10362591478871}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}e$ |
| 29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $\phantom{-}\frac{2021885932}{31087774436613}e^{11} - \frac{219911362576}{31087774436613}e^{9} + \frac{2786186160727}{10362591478871}e^{7} - \frac{128218626448336}{31087774436613}e^{5} + \frac{223143091022717}{10362591478871}e^{3} - \frac{669980918789692}{31087774436613}e$ |
| 29 | $[29, 29, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{147143617}{10362591478871}e^{10} - \frac{18422484787}{10362591478871}e^{8} + \frac{782709511517}{10362591478871}e^{6} - \frac{13087539707115}{10362591478871}e^{4} + \frac{72713333341728}{10362591478871}e^{2} - \frac{14257329906810}{10362591478871}$ |
| 31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{1400328235}{31087774436613}e^{11} + \frac{149696322586}{31087774436613}e^{9} - \frac{1845708861417}{10362591478871}e^{7} + \frac{80370857188150}{31087774436613}e^{5} - \frac{119099245590007}{10362591478871}e^{3} + \frac{206094330601900}{31087774436613}e$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1841187694}{93263323309839}e^{11} - \frac{200741106163}{93263323309839}e^{9} + \frac{2518738935229}{31087774436613}e^{7} - \frac{112011560339005}{93263323309839}e^{5} + \frac{180273578838490}{31087774436613}e^{3} - \frac{722581311470086}{93263323309839}e$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{4726406617}{93263323309839}e^{11} - \frac{515703318316}{93263323309839}e^{9} + \frac{6528845124595}{31087774436613}e^{7} - \frac{296675754650401}{93263323309839}e^{5} + \frac{486030167820835}{31087774436613}e^{3} - \frac{1085690644903327}{93263323309839}e$ |
| 43 | $[43, 43, -w^{2} - w + 4]$ | $\phantom{-}\frac{863894581}{10362591478871}e^{10} - \frac{92236974965}{10362591478871}e^{8} + \frac{3451409448426}{10362591478871}e^{6} - \frac{52292092845468}{10362591478871}e^{4} + \frac{267770803238970}{10362591478871}e^{2} - \frac{189967673569055}{10362591478871}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $-\frac{135452473}{10362591478871}e^{10} + \frac{15592500003}{10362591478871}e^{8} - \frac{575251781079}{10362591478871}e^{6} + \frac{7235226319510}{10362591478871}e^{4} - \frac{20577418103263}{10362591478871}e^{2} + \frac{33345203756941}{10362591478871}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-\frac{572068676}{31087774436613}e^{11} + \frac{63135427361}{31087774436613}e^{9} - \frac{829246563216}{10362591478871}e^{7} + \frac{41482229487905}{31087774436613}e^{5} - \frac{88621662868844}{10362591478871}e^{3} + \frac{455702294407958}{31087774436613}e$ |
| 73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $-\frac{8425454807}{93263323309839}e^{11} + \frac{908081949323}{93263323309839}e^{9} - \frac{11376946131203}{31087774436613}e^{7} + \frac{513756890570453}{93263323309839}e^{5} - \frac{846453430999682}{31087774436613}e^{3} + \frac{1905644436704690}{93263323309839}e$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{184755931}{10362591478871}e^{10} - \frac{24782828402}{10362591478871}e^{8} + \frac{1073959026959}{10362591478871}e^{6} - \frac{16947822929002}{10362591478871}e^{4} + \frac{67829606900876}{10362591478871}e^{2} + \frac{57865617915442}{10362591478871}$ |
| 81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $-\frac{10681745698}{93263323309839}e^{11} + \frac{1143627960214}{93263323309839}e^{9} - \frac{14101998902026}{31087774436613}e^{7} + \frac{613052829218923}{93263323309839}e^{5} - \frac{901686843495553}{31087774436613}e^{3} + \frac{1018308624797410}{93263323309839}e$ |
| 83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $-\frac{3535622501}{93263323309839}e^{11} + \frac{392911386791}{93263323309839}e^{9} - \frac{5032823975291}{31087774436613}e^{7} + \frac{227792249272637}{93263323309839}e^{5} - \frac{348897610265117}{31087774436613}e^{3} + \frac{92728091467241}{93263323309839}e$ |
| 89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{6716061374}{93263323309839}e^{11} + \frac{737683262366}{93263323309839}e^{9} - \frac{9381276268106}{31087774436613}e^{7} + \frac{427783934306249}{93263323309839}e^{5} - \frac{712570294350923}{31087774436613}e^{3} + \frac{1739561514403076}{93263323309839}e$ |
| 97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-\frac{744942999}{10362591478871}e^{10} + \frac{83680714051}{10362591478871}e^{8} - \frac{3244561548464}{10362591478871}e^{6} + \frac{50037100372472}{10362591478871}e^{4} - \frac{259657088696827}{10362591478871}e^{2} + \frac{222501437110285}{10362591478871}$ |
| 101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $\phantom{-}\frac{255732402}{10362591478871}e^{10} - \frac{30483386715}{10362591478871}e^{8} + \frac{1275161269673}{10362591478871}e^{6} - \frac{21386993896275}{10362591478871}e^{4} + \frac{117664675056603}{10362591478871}e^{2} - \frac{85409806470806}{10362591478871}$ |
| 103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $\phantom{-}\frac{14491112603}{93263323309839}e^{11} - \frac{1567816037051}{93263323309839}e^{9} + \frac{19735504613384}{31087774436613}e^{7} - \frac{898412769915461}{93263323309839}e^{5} + \frac{1515882704067833}{31087774436613}e^{3} - \frac{3729060546454088}{93263323309839}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^{2} - w - 2]$ | $-1$ |