Base field 6.6.1683101.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49, 7, -w^{5} + 4w^{4} - w^{3} - 11w^{2} + 7w + 7]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 60x^{14} + 1356x^{12} - 14680x^{10} + 80848x^{8} - 224640x^{6} + 298752x^{4} - 153600x^{2} + 4096\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{2} - 3]$ | $\phantom{-}\frac{77331}{142825472}e^{15} - \frac{71493}{2231648}e^{13} + \frac{25252325}{35706368}e^{11} - \frac{131072627}{17853184}e^{9} + \frac{332940865}{8926592}e^{7} - \frac{195256973}{2231648}e^{5} + \frac{44350821}{557912}e^{3} - \frac{1983575}{139478}e$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{597}{35706368}e^{14} - \frac{21977}{17853184}e^{12} + \frac{313433}{8926592}e^{10} - \frac{545605}{1115824}e^{8} + \frac{3863101}{1115824}e^{6} - \frac{13390335}{1115824}e^{4} + \frac{2551589}{139478}e^{2} - \frac{446274}{69739}$ |
| 29 | $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ | $-\frac{93023}{142825472}e^{15} + \frac{1365549}{35706368}e^{13} - \frac{29764413}{35706368}e^{11} + \frac{151056669}{17853184}e^{9} - \frac{367590491}{8926592}e^{7} + \frac{98100147}{1115824}e^{5} - \frac{33243285}{557912}e^{3} - \frac{773582}{69739}e$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ | $-\frac{2643}{557912}e^{15} + \frac{9883951}{35706368}e^{13} - \frac{53473925}{8926592}e^{11} + \frac{537262001}{8926592}e^{9} - \frac{1291715477}{4463296}e^{7} + \frac{1379886623}{2231648}e^{5} - \frac{67393591}{139478}e^{3} + \frac{2875296}{69739}e$ |
| 41 | $[41, 41, -w^{2} + 4]$ | $\phantom{-}\frac{12345}{35706368}e^{14} - \frac{368239}{17853184}e^{12} + \frac{4126285}{8926592}e^{10} - \frac{11018283}{2231648}e^{8} + \frac{14766105}{557912}e^{6} - \frac{75827101}{1115824}e^{4} + \frac{9215483}{139478}e^{2} - \frac{256429}{69739}$ |
| 41 | $[41, 41, -w^{2} + 2w + 3]$ | $-\frac{130927}{35706368}e^{15} + \frac{7654423}{35706368}e^{13} - \frac{10362305}{2231648}e^{11} + \frac{417127663}{8926592}e^{9} - \frac{1006004467}{4463296}e^{7} + \frac{1081250439}{2231648}e^{5} - \frac{106604683}{278956}e^{3} + \frac{2137076}{69739}e$ |
| 43 | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $\phantom{-}\frac{162839}{35706368}e^{15} - \frac{4761153}{17853184}e^{13} + \frac{51578009}{8926592}e^{11} - \frac{129784847}{2231648}e^{9} + \frac{312752681}{1115824}e^{7} - \frac{668206125}{1115824}e^{5} + \frac{127317377}{278956}e^{3} - \frac{1696372}{69739}e$ |
| 43 | $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $-\frac{173853}{71412736}e^{15} + \frac{2528691}{17853184}e^{13} - \frac{54324699}{17853184}e^{11} + \frac{269327119}{8926592}e^{9} - \frac{630723445}{4463296}e^{7} + \frac{79169905}{278956}e^{5} - \frac{25313907}{139478}e^{3} - \frac{1678958}{69739}e$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{251203}{71412736}e^{14} - \frac{3657217}{17853184}e^{12} + \frac{78727469}{17853184}e^{10} - \frac{392143161}{8926592}e^{8} + \frac{929667419}{4463296}e^{6} - \frac{30299621}{69739}e^{4} + \frac{22671857}{69739}e^{2} - \frac{972662}{69739}$ |
| 71 | $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ | $\phantom{-}\frac{272899}{71412736}e^{15} - \frac{3975955}{17853184}e^{13} + \frac{85646453}{17853184}e^{11} - \frac{426488045}{8926592}e^{9} + \frac{1005877927}{4463296}e^{7} - \frac{254819127}{557912}e^{5} + \frac{39991015}{139478}e^{3} + \frac{4020329}{69739}e$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ | $\phantom{-}\frac{392055}{71412736}e^{15} - \frac{5732273}{17853184}e^{13} + \frac{124197445}{17853184}e^{11} - \frac{624728229}{8926592}e^{9} + \frac{1502107779}{4463296}e^{7} - \frac{397765379}{557912}e^{5} + \frac{146285939}{278956}e^{3} - \frac{476575}{69739}e$ |
| 71 | $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $\phantom{-}\frac{45727}{35706368}e^{15} - \frac{1349461}{17853184}e^{13} + \frac{14855475}{8926592}e^{11} - \frac{38514841}{2231648}e^{9} + \frac{24662799}{278956}e^{7} - \frac{242485551}{1115824}e^{5} + \frac{16597202}{69739}e^{3} - \frac{5856948}{69739}e$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ | $-\frac{29635}{8926592}e^{15} + \frac{862911}{4463296}e^{13} - \frac{18567211}{4463296}e^{11} + \frac{46144553}{1115824}e^{9} - \frac{217000875}{1115824}e^{7} + \frac{218782679}{557912}e^{5} - \frac{68649441}{278956}e^{3} - \frac{2761233}{69739}e$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ | $\phantom{-}\frac{171135}{35706368}e^{14} - \frac{156143}{557912}e^{12} + \frac{54010733}{8926592}e^{10} - \frac{270902567}{4463296}e^{8} + \frac{649446657}{2231648}e^{6} - \frac{343972835}{557912}e^{4} + \frac{32091478}{69739}e^{2} - \frac{985640}{69739}$ |
| 83 | $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ | $\phantom{-}\frac{38707}{8926592}e^{15} - \frac{4553043}{17853184}e^{13} + \frac{6223981}{1115824}e^{11} - \frac{254730237}{4463296}e^{9} + \frac{632994559}{2231648}e^{7} - \frac{721336689}{1115824}e^{5} + \frac{162046933}{278956}e^{3} - \frac{8221698}{69739}e$ |
| 97 | $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $\phantom{-}\frac{166985}{71412736}e^{15} - \frac{4861911}{35706368}e^{13} + \frac{52303863}{17853184}e^{11} - \frac{130016223}{4463296}e^{9} + \frac{306290465}{2231648}e^{7} - \frac{625464479}{2231648}e^{5} + \frac{108485877}{557912}e^{3} - \frac{178078}{69739}e$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ | $\phantom{-}\frac{125069}{17853184}e^{14} - \frac{7300461}{17853184}e^{12} + \frac{9855499}{1115824}e^{10} - \frac{394614021}{4463296}e^{8} + \frac{941248465}{2231648}e^{6} - \frac{986069309}{1115824}e^{4} + \frac{90621323}{139478}e^{2} - \frac{764416}{69739}$ |
| 113 | $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ | $\phantom{-}\frac{85109}{35706368}e^{14} - \frac{1245465}{8926592}e^{12} + \frac{27010545}{8926592}e^{10} - \frac{135976271}{4463296}e^{8} + \frac{327032131}{2231648}e^{6} - \frac{173350975}{557912}e^{4} + \frac{65002195}{278956}e^{2} - \frac{774926}{69739}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $1$ |