Base field 6.6.1229312.1
Generator \(w\), with minimal polynomial \(x^{6} - 10x^{4} + 24x^{2} - 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41,41,\frac{1}{2}w^{2} + w - 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 10x^{6} + 17x^{5} - 113x^{4} - 461x^{3} - 507x^{2} - 91x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $\phantom{-}\frac{744}{10457}e^{6} + \frac{7303}{10457}e^{5} + \frac{9715}{10457}e^{4} - \frac{92003}{10457}e^{3} - \frac{300898}{10457}e^{2} - \frac{235924}{10457}e - \frac{20944}{10457}$ |
| 7 | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}e$ |
| 8 | $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ | $\phantom{-}\frac{174}{10457}e^{6} + \frac{443}{10457}e^{5} - \frac{6414}{10457}e^{4} - \frac{16204}{10457}e^{3} + \frac{55956}{10457}e^{2} + \frac{140134}{10457}e + \frac{9944}{10457}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} - \frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 1]$ | $-\frac{2124}{10457}e^{6} - \frac{17307}{10457}e^{5} - \frac{9688}{10457}e^{4} + \frac{222681}{10457}e^{3} + \frac{605686}{10457}e^{2} + \frac{473830}{10457}e - \frac{11046}{10457}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + 2w^{2} - 5w - 2]$ | $-\frac{516}{10457}e^{6} - \frac{4559}{10457}e^{5} - \frac{1172}{10457}e^{4} + \frac{70049}{10457}e^{3} + \frac{124694}{10457}e^{2} - \frac{12795}{10457}e + \frac{67148}{10457}$ |
| 41 | $[41, 41, \frac{1}{4}w^{5} - \frac{1}{4}w^{4} - \frac{5}{2}w^{3} + 2w^{2} + 5w - 2]$ | $-\frac{1623}{10457}e^{6} - \frac{15130}{10457}e^{5} - \frac{20223}{10457}e^{4} + \frac{177467}{10457}e^{3} + \frac{638432}{10457}e^{2} + \frac{654477}{10457}e + \frac{97636}{10457}$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - w - 2]$ | $\phantom{-}\frac{1525}{10457}e^{6} + \frac{12116}{10457}e^{5} + \frac{5085}{10457}e^{4} - \frac{158124}{10457}e^{3} - \frac{404556}{10457}e^{2} - \frac{305868}{10457}e - \frac{99150}{10457}$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 1]$ | $\phantom{-}\frac{802}{10457}e^{6} + \frac{3965}{10457}e^{5} - \frac{13337}{10457}e^{4} - \frac{69519}{10457}e^{3} + \frac{21007}{10457}e^{2} + \frac{159354}{10457}e - \frac{31572}{10457}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + w^{2} - 5w + 1]$ | $-\frac{1631}{10457}e^{6} - \frac{14309}{10457}e^{5} - \frac{17404}{10457}e^{4} + \frac{162827}{10457}e^{3} + \frac{607373}{10457}e^{2} + \frac{686136}{10457}e + \frac{65928}{10457}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + \frac{3}{2}w^{2} - 6w - 2]$ | $\phantom{-}\frac{2188}{10457}e^{6} + \frac{21196}{10457}e^{5} + \frac{28964}{10457}e^{4} - \frac{262416}{10457}e^{3} - \frac{900978}{10457}e^{2} - \frac{748016}{10457}e - \frac{28086}{10457}$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} - \frac{1}{2}w^{3} - \frac{5}{2}w^{2} + 3w + 4]$ | $-\frac{3233}{10457}e^{6} - \frac{30287}{10457}e^{5} - \frac{35877}{10457}e^{4} + \frac{378724}{10457}e^{3} + \frac{1224072}{10457}e^{2} + \frac{1015690}{10457}e + \frac{63800}{10457}$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - 3w + 4]$ | $-\frac{2219}{10457}e^{6} - \frac{21936}{10457}e^{5} - \frac{35033}{10457}e^{4} + \frac{257971}{10457}e^{3} + \frac{985843}{10457}e^{2} + \frac{947815}{10457}e + \frac{119586}{10457}$ |
| 71 | $[71, 71, \frac{1}{2}w^{4} - \frac{7}{2}w^{2} + w + 3]$ | $\phantom{-}\frac{3244}{10457}e^{6} + \frac{27851}{10457}e^{5} + \frac{22851}{10457}e^{4} - \frac{358594}{10457}e^{3} - \frac{1046732}{10457}e^{2} - \frac{754661}{10457}e - \frac{4516}{10457}$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + \frac{5}{2}w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}\frac{1260}{10457}e^{6} + \frac{11862}{10457}e^{5} + \frac{10887}{10457}e^{4} - \frac{162052}{10457}e^{3} - \frac{436049}{10457}e^{2} - \frac{212672}{10457}e - \frac{4436}{10457}$ |
| 97 | $[97, 97, \frac{1}{4}w^{5} - \frac{5}{2}w^{3} - \frac{1}{2}w^{2} + 5w]$ | $-\frac{1523}{10457}e^{6} - \frac{9707}{10457}e^{5} + \frac{12510}{10457}e^{4} + \frac{151327}{10457}e^{3} + \frac{143053}{10457}e^{2} - \frac{133398}{10457}e - \frac{49778}{10457}$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{3}{2}w^{2} + w + 1]$ | $-\frac{1066}{10457}e^{6} - \frac{8243}{10457}e^{5} + \frac{1794}{10457}e^{4} + \frac{130163}{10457}e^{3} + \frac{219343}{10457}e^{2} - \frac{108022}{10457}e - \frac{136404}{10457}$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + 2w^{2} - 3w - 4]$ | $-\frac{2064}{10457}e^{6} - \frac{18236}{10457}e^{5} - \frac{15145}{10457}e^{4} + \frac{238368}{10457}e^{3} + \frac{676545}{10457}e^{2} + \frac{482127}{10457}e - \frac{66032}{10457}$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - 2w^{2} - 3w + 4]$ | $-\frac{1091}{10457}e^{6} - \frac{12213}{10457}e^{5} - \frac{24689}{10457}e^{4} + \frac{136698}{10457}e^{3} + \frac{586313}{10457}e^{2} + \frac{656239}{10457}e + \frac{93904}{10457}$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} - \frac{3}{2}w^{2} + w - 1]$ | $\phantom{-}\frac{2526}{10457}e^{6} + \frac{20494}{10457}e^{5} + \frac{1360}{10457}e^{4} - \frac{302667}{10457}e^{3} - \frac{579536}{10457}e^{2} - \frac{17737}{10457}e + \frac{192678}{10457}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41,41,\frac{1}{2}w^{2} + w - 2]$ | $-1$ |