Base field 4.4.5725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 2x^{5} - 41x^{4} - 47x^{3} + 358x^{2} + 10x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w + 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{1112}{27829}e^{5} + \frac{1328}{27829}e^{4} - \frac{45661}{27829}e^{3} - \frac{24682}{27829}e^{2} + \frac{398163}{27829}e - \frac{41022}{27829}$ |
| 11 | $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ | $-\frac{346}{27829}e^{5} - \frac{213}{27829}e^{4} + \frac{13757}{27829}e^{3} - \frac{4633}{27829}e^{2} - \frac{107722}{27829}e + \frac{111567}{27829}$ |
| 11 | $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ | $\phantom{-}\frac{1112}{27829}e^{5} + \frac{1328}{27829}e^{4} - \frac{45661}{27829}e^{3} - \frac{24682}{27829}e^{2} + \frac{398163}{27829}e - \frac{41022}{27829}$ |
| 11 | $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ | $-\frac{346}{27829}e^{5} - \frac{213}{27829}e^{4} + \frac{13757}{27829}e^{3} - \frac{4633}{27829}e^{2} - \frac{107722}{27829}e + \frac{111567}{27829}$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 25 | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $\phantom{-}\frac{985}{27829}e^{5} + \frac{2778}{27829}e^{4} - \frac{33614}{27829}e^{3} - \frac{71665}{27829}e^{2} + \frac{186341}{27829}e + \frac{232293}{27829}$ |
| 29 | $[29, 29, -w - 3]$ | $\phantom{-}\frac{3005}{27829}e^{5} + \frac{5791}{27829}e^{4} - \frac{124868}{27829}e^{3} - \frac{139525}{27829}e^{2} + \frac{1090311}{27829}e + \frac{50663}{27829}$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $\phantom{-}\frac{3005}{27829}e^{5} + \frac{5791}{27829}e^{4} - \frac{124868}{27829}e^{3} - \frac{139525}{27829}e^{2} + \frac{1090311}{27829}e + \frac{50663}{27829}$ |
| 31 | $[31, 31, w^{3} - 6w + 1]$ | $-\frac{3212}{27829}e^{5} - \frac{5838}{27829}e^{4} + \frac{136396}{27829}e^{3} + \frac{138764}{27829}e^{2} - \frac{1256100}{27829}e - \frac{34668}{27829}$ |
| 31 | $[31, 31, w^{3} - 6w - 2]$ | $-\frac{3212}{27829}e^{5} - \frac{5838}{27829}e^{4} + \frac{136396}{27829}e^{3} + \frac{138764}{27829}e^{2} - \frac{1256100}{27829}e - \frac{34668}{27829}$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $-\frac{1192}{27829}e^{5} - \frac{2825}{27829}e^{4} + \frac{45142}{27829}e^{3} + \frac{70904}{27829}e^{2} - \frac{352130}{27829}e - \frac{49324}{27829}$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ | $-\frac{1192}{27829}e^{5} - \frac{2825}{27829}e^{4} + \frac{45142}{27829}e^{3} + \frac{70904}{27829}e^{2} - \frac{352130}{27829}e - \frac{49324}{27829}$ |
| 59 | $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ | $\phantom{-}\frac{4697}{27829}e^{5} + \frac{11015}{27829}e^{4} - \frac{187638}{27829}e^{3} - \frac{262770}{27829}e^{2} + \frac{1579127}{27829}e + \frac{94155}{27829}$ |
| 59 | $[59, 59, w^{3} + w^{2} - 6w - 4]$ | $\phantom{-}\frac{4697}{27829}e^{5} + \frac{11015}{27829}e^{4} - \frac{187638}{27829}e^{3} - \frac{262770}{27829}e^{2} + \frac{1579127}{27829}e + \frac{94155}{27829}$ |
| 79 | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $-\frac{1680}{27829}e^{5} - \frac{3608}{27829}e^{4} + \frac{72588}{27829}e^{3} + \frac{80134}{27829}e^{2} - \frac{675218}{27829}e + \frac{106422}{27829}$ |
| 79 | $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ | $-\frac{1680}{27829}e^{5} - \frac{3608}{27829}e^{4} + \frac{72588}{27829}e^{3} + \frac{80134}{27829}e^{2} - \frac{675218}{27829}e + \frac{106422}{27829}$ |
| 89 | $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ | $-\frac{4969}{27829}e^{5} - \frac{10539}{27829}e^{4} + \frac{197005}{27829}e^{3} + \frac{247385}{27829}e^{2} - \frac{1611852}{27829}e + \frac{32801}{27829}$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ | $-\frac{4969}{27829}e^{5} - \frac{10539}{27829}e^{4} + \frac{197005}{27829}e^{3} + \frac{247385}{27829}e^{2} - \frac{1611852}{27829}e + \frac{32801}{27829}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |