Base field 4.4.19525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 4x^{7} - 13x^{6} + 48x^{5} + 46x^{4} - 110x^{3} - 59x^{2} + 26x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ | $\phantom{-}e$ |
| 5 | $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ | $\phantom{-}\frac{531}{6224}e^{7} - \frac{1885}{6224}e^{6} - \frac{1029}{778}e^{5} + \frac{2969}{778}e^{4} + \frac{20137}{3112}e^{3} - \frac{3829}{389}e^{2} - \frac{69441}{6224}e + \frac{17961}{6224}$ |
| 9 | $[9, 3, -w + 3]$ | $\phantom{-}\frac{297}{3112}e^{7} - \frac{1173}{3112}e^{6} - \frac{1039}{778}e^{5} + \frac{3763}{778}e^{4} + \frac{8217}{1556}e^{3} - \frac{5147}{389}e^{2} - \frac{21803}{3112}e + \frac{13725}{3112}$ |
| 9 | $[9, 3, w + 2]$ | $\phantom{-}\frac{157}{1556}e^{7} - \frac{156}{389}e^{6} - \frac{995}{778}e^{5} + \frac{3537}{778}e^{4} + \frac{1718}{389}e^{3} - \frac{3160}{389}e^{2} - \frac{7811}{1556}e - \frac{893}{778}$ |
| 11 | $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{531}{6224}e^{7} - \frac{1885}{6224}e^{6} - \frac{1029}{778}e^{5} + \frac{2969}{778}e^{4} + \frac{20137}{3112}e^{3} - \frac{3829}{389}e^{2} - \frac{63217}{6224}e + \frac{11737}{6224}$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ | $-\frac{21}{389}e^{7} + \frac{485}{1556}e^{6} + \frac{183}{778}e^{5} - \frac{2549}{778}e^{4} + \frac{1955}{778}e^{3} + \frac{1713}{389}e^{2} - \frac{2258}{389}e + \frac{1741}{1556}$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ | $-\frac{151}{3112}e^{7} + \frac{895}{3112}e^{6} + \frac{227}{778}e^{5} - \frac{2775}{778}e^{4} + \frac{2565}{1556}e^{3} + \frac{3700}{389}e^{2} - \frac{11883}{3112}e - \frac{13815}{3112}$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ | $-\frac{113}{778}e^{7} + \frac{407}{778}e^{6} + \frac{788}{389}e^{5} - \frac{2350}{389}e^{4} - \frac{3256}{389}e^{3} + \frac{4970}{389}e^{2} + \frac{9393}{778}e - \frac{2275}{778}$ |
| 29 | $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $\phantom{-}\frac{1143}{3112}e^{7} - \frac{4585}{3112}e^{6} - \frac{1793}{389}e^{5} + \frac{6681}{389}e^{4} + \frac{23065}{1556}e^{3} - \frac{13926}{389}e^{2} - \frac{49205}{3112}e + \frac{17669}{3112}$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ | $-\frac{2219}{6224}e^{7} + \frac{9149}{6224}e^{6} + \frac{3421}{778}e^{5} - \frac{13487}{778}e^{4} - \frac{44017}{3112}e^{3} + \frac{14741}{389}e^{2} + \frac{118377}{6224}e - \frac{28729}{6224}$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ | $\phantom{-}\frac{605}{3112}e^{7} - \frac{2303}{3112}e^{6} - \frac{979}{389}e^{5} + \frac{3278}{389}e^{4} + \frac{13367}{1556}e^{3} - \frac{6148}{389}e^{2} - \frac{31735}{3112}e + \frac{5915}{3112}$ |
| 49 | $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ | $\phantom{-}\frac{43}{1556}e^{7} - \frac{327}{1556}e^{6} - \frac{26}{389}e^{5} + \frac{1053}{389}e^{4} - \frac{885}{778}e^{3} - \frac{3586}{389}e^{2} - \frac{841}{1556}e + \frac{16887}{1556}$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ | $\phantom{-}\frac{411}{6224}e^{7} - \frac{2637}{6224}e^{6} - \frac{269}{778}e^{5} + \frac{4087}{778}e^{4} - \frac{4967}{3112}e^{3} - \frac{5579}{389}e^{2} - \frac{11657}{6224}e + \frac{54569}{6224}$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ | $-\frac{1751}{3112}e^{7} + \frac{7725}{3112}e^{6} + \frac{2402}{389}e^{5} - \frac{11312}{389}e^{4} - \frac{20177}{1556}e^{3} + \frac{24460}{389}e^{2} + \frac{29325}{3112}e - \frac{38929}{3112}$ |
| 59 | $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ | $\phantom{-}\frac{1113}{3112}e^{7} - \frac{3995}{3112}e^{6} - \frac{1992}{389}e^{5} + \frac{5988}{389}e^{4} + \frac{33127}{1556}e^{3} - \frac{13634}{389}e^{2} - \frac{89219}{3112}e + \frac{18263}{3112}$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ | $-\frac{493}{778}e^{7} + \frac{3961}{1556}e^{6} + \frac{6177}{778}e^{5} - \frac{23187}{778}e^{4} - \frac{19629}{778}e^{3} + \frac{24692}{389}e^{2} + \frac{19141}{778}e - \frac{17899}{1556}$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ | $\phantom{-}\frac{1319}{3112}e^{7} - \frac{5453}{3112}e^{6} - \frac{2000}{389}e^{5} + \frac{7868}{389}e^{4} + \frac{23785}{1556}e^{3} - \frac{15276}{389}e^{2} - \frac{49101}{3112}e + \frac{7649}{3112}$ |
| 61 | $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ | $\phantom{-}\frac{377}{1556}e^{7} - \frac{1709}{1556}e^{6} - \frac{1015}{389}e^{5} + \frac{5125}{389}e^{4} + \frac{3169}{778}e^{3} - \frac{11592}{389}e^{2} + \frac{7101}{1556}e + \frac{12141}{1556}$ |
| 61 | $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ | $\phantom{-}\frac{335}{1556}e^{7} - \frac{318}{389}e^{6} - \frac{2133}{778}e^{5} + \frac{7225}{778}e^{4} + \frac{3532}{389}e^{3} - \frac{7429}{389}e^{2} - \frac{13753}{1556}e + \frac{4269}{778}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ | $1$ |