Base field 4.4.18625.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 14 x^2 + 9 x + 41\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9,3,w + 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^7 + 4 x^6 - 11 x^5 - 44 x^4 + 42 x^3 + 105 x^2 - 110 x + 20\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{6} w^3 - \frac{7}{3} w - \frac{17}{6}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w - 3]$ | $-\frac{7}{139} e^6 + \frac{13}{139} e^5 + \frac{120}{139} e^4 - \frac{236}{139} e^3 - \frac{401}{139} e^2 + \frac{1018}{139} e - \frac{685}{139}$ |
| 5 | $[5, 5, -\frac{1}{6} w^3 + w^2 + \frac{1}{3} w - \frac{25}{6}]$ | $-\frac{15}{278} e^6 + \frac{4}{139} e^5 + \frac{277}{278} e^4 - \frac{94}{139} e^3 - \frac{658}{139} e^2 + \frac{851}{278} e + \frac{110}{139}$ |
| 9 | $[9, 3, \frac{1}{6} w^3 - \frac{7}{3} w + \frac{13}{6}]$ | $\phantom{-}\frac{35}{278} e^6 + \frac{37}{139} e^5 - \frac{461}{278} e^4 - \frac{383}{139} e^3 + \frac{794}{139} e^2 + \frac{1721}{278} e - \frac{720}{139}$ |
| 9 | $[9, 3, -w - 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -\frac{1}{6} w^3 + \frac{7}{3} w + \frac{11}{6}]$ | $\phantom{-}\frac{13}{278} e^6 - \frac{22}{139} e^5 - \frac{203}{278} e^4 + \frac{517}{139} e^3 + \frac{283}{139} e^2 - \frac{5167}{278} e + \frac{1341}{139}$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}\frac{7}{139} e^6 - \frac{13}{139} e^5 - \frac{120}{139} e^4 + \frac{236}{139} e^3 + \frac{401}{139} e^2 - \frac{1157}{139} e + \frac{546}{139}$ |
| 41 | $[41, 41, -w]$ | $\phantom{-}\frac{29}{278} e^6 - \frac{156}{139} e^5 - \frac{1073}{278} e^4 + \frac{1998}{139} e^3 + \frac{2866}{139} e^2 - \frac{13451}{278} e + \frac{1826}{139}$ |
| 41 | $[41, 41, \frac{1}{6} w^3 - \frac{7}{3} w + \frac{1}{6}]$ | $\phantom{-}\frac{113}{278} e^6 + \frac{322}{139} e^5 - \frac{567}{278} e^4 - \frac{3397}{139} e^3 - \frac{566}{139} e^2 + \frac{15199}{278} e - \frac{3099}{139}$ |
| 59 | $[59, 59, -\frac{1}{6} w^3 + \frac{1}{3} w + \frac{23}{6}]$ | $-\frac{187}{278} e^6 - \frac{293}{139} e^5 + \frac{1637}{278} e^4 + \frac{2368}{139} e^3 - \frac{799}{139} e^2 - \frac{3087}{278} e - \frac{1455}{139}$ |
| 59 | $[59, 59, -\frac{1}{3} w^3 + \frac{11}{3} w + \frac{11}{3}]$ | $\phantom{-}\frac{18}{139} e^6 + \frac{185}{139} e^5 + \frac{168}{139} e^4 - \frac{1915}{139} e^3 - \frac{2424}{139} e^2 + \frac{4372}{139} e + \frac{570}{139}$ |
| 61 | $[61, 61, -\frac{5}{3} w^3 - 3 w^2 + \frac{46}{3} w + \frac{79}{3}]$ | $\phantom{-}\frac{53}{139} e^6 + \frac{120}{139} e^5 - \frac{710}{139} e^4 - \frac{1152}{139} e^3 + \frac{2361}{139} e^2 + \frac{1645}{139} e - \frac{314}{139}$ |
| 61 | $[61, 61, \frac{5}{6} w^3 + w^2 - \frac{23}{3} w - \frac{55}{6}]$ | $\phantom{-}\frac{57}{278} e^6 + \frac{235}{139} e^5 + \frac{115}{278} e^4 - \frac{2534}{139} e^3 - \frac{1753}{139} e^2 + \frac{12779}{278} e - \frac{1669}{139}$ |
| 61 | $[61, 61, w^3 + 2 w^2 - 9 w - 17]$ | $\phantom{-}\frac{31}{278} e^6 - \frac{138}{139} e^5 - \frac{1147}{278} e^4 + \frac{1714}{139} e^3 + \frac{3241}{139} e^2 - \frac{10803}{278} e + \frac{931}{139}$ |
| 61 | $[61, 61, -\frac{1}{6} w^3 + \frac{10}{3} w + \frac{35}{6}]$ | $\phantom{-}\frac{112}{139} e^6 + \frac{348}{139} e^5 - \frac{1225}{139} e^4 - \frac{3174}{139} e^3 + \frac{3497}{139} e^2 + \frac{4562}{139} e - \frac{2384}{139}$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + 2 w^2 + 4 w - \frac{33}{2}]$ | $-\frac{97}{139} e^6 - \frac{356}{139} e^5 + \frac{948}{139} e^4 + \frac{3362}{139} e^3 - \frac{2320}{139} e^2 - \frac{5413}{139} e + \frac{3276}{139}$ |
| 71 | $[71, 71, \frac{1}{6} w^3 - w^2 - \frac{4}{3} w + \frac{67}{6}]$ | $\phantom{-}\frac{15}{139} e^6 + \frac{131}{139} e^5 - \frac{138}{139} e^4 - \frac{1897}{139} e^3 + \frac{621}{139} e^2 + \frac{6794}{139} e - \frac{3834}{139}$ |
| 79 | $[79, 79, \frac{1}{2} w^3 - 3 w + \frac{1}{2}]$ | $-\frac{227}{278} e^6 - \frac{375}{139} e^5 + \frac{2283}{278} e^4 + \frac{3461}{139} e^3 - \frac{2600}{139} e^2 - \frac{10177}{278} e + \frac{1850}{139}$ |
| 79 | $[79, 79, -\frac{2}{3} w^3 + \frac{19}{3} w - \frac{2}{3}]$ | $-\frac{13}{278} e^6 - \frac{256}{139} e^5 - \frac{909}{278} e^4 + \frac{2958}{139} e^3 + \frac{3748}{139} e^2 - \frac{15405}{278} e + \frac{605}{139}$ |
| 89 | $[89, 89, \frac{1}{2} w^3 + w^2 - 5 w - \frac{15}{2}]$ | $-\frac{53}{278} e^6 + \frac{79}{139} e^5 + \frac{1127}{278} e^4 - \frac{1231}{139} e^3 - \frac{2640}{139} e^2 + \frac{9475}{278} e - \frac{1650}{139}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9,3,w + 2]$ | $-1$ |