Base field 4.4.14725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 11x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11,11,-\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{13}{3}]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 7x^{4} - 3x^{3} + 100x^{2} - 141x - 77\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{11}{3}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w - 2]$ | $-\frac{1}{3}e^{4} + e^{3} + \frac{14}{3}e^{2} - \frac{41}{3}e - 1$ |
| 11 | $[11, 11, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{8}{3}]$ | $\phantom{-}e^{4} - \frac{10}{3}e^{3} - 15e^{2} + \frac{131}{3}e + \frac{61}{3}$ |
| 11 | $[11, 11, \frac{2}{3}w^{3} + \frac{2}{3}w^{2} - \frac{19}{3}w - \frac{13}{3}]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{2}{3}e^{4} - 2e^{3} - \frac{31}{3}e^{2} + \frac{82}{3}e + 15$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{2}{3}e^{4} - 2e^{3} - \frac{31}{3}e^{2} + \frac{79}{3}e + 20$ |
| 25 | $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ | $-\frac{2}{3}e^{4} + 2e^{3} + \frac{31}{3}e^{2} - \frac{79}{3}e - 17$ |
| 29 | $[29, 29, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{19}{3}]$ | $\phantom{-}2e^{4} - \frac{19}{3}e^{3} - 30e^{2} + \frac{248}{3}e + \frac{124}{3}$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{14}{3}]$ | $\phantom{-}\frac{2}{3}e^{4} - 3e^{3} - \frac{31}{3}e^{2} + \frac{121}{3}e + 18$ |
| 29 | $[29, 29, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - \frac{8}{3}]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{14}{3}e + \frac{11}{3}$ |
| 29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{4}{3}e^{4} - 5e^{3} - \frac{59}{3}e^{2} + \frac{200}{3}e + 21$ |
| 31 | $[31, 31, w]$ | $-2e^{4} + \frac{22}{3}e^{3} + 30e^{2} - \frac{293}{3}e - \frac{121}{3}$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{8}{3}w + \frac{13}{3}]$ | $\phantom{-}\frac{2}{3}e^{4} - \frac{7}{3}e^{3} - \frac{31}{3}e^{2} + 30e + \frac{55}{3}$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{5}{3}]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{4}{3}e^{3} - \frac{14}{3}e^{2} + \frac{52}{3}e + \frac{28}{3}$ |
| 41 | $[41, 41, \frac{1}{3}w^{3} + \frac{4}{3}w^{2} - \frac{8}{3}w - \frac{20}{3}]$ | $\phantom{-}\frac{1}{3}e^{3} - e^{2} - \frac{11}{3}e + \frac{32}{3}$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{40}{3}]$ | $-\frac{1}{3}e^{4} + \frac{2}{3}e^{3} + \frac{17}{3}e^{2} - 10e - \frac{35}{3}$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{8}{3}w + \frac{38}{3}]$ | $-\frac{4}{3}e^{4} + 5e^{3} + \frac{62}{3}e^{2} - \frac{203}{3}e - 30$ |
| 49 | $[49, 7, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{43}{3}]$ | $-\frac{4}{3}e^{4} + \frac{13}{3}e^{3} + \frac{59}{3}e^{2} - \frac{172}{3}e - \frac{67}{3}$ |
| 59 | $[59, 59, \frac{5}{3}w^{3} + \frac{8}{3}w^{2} - \frac{40}{3}w - \frac{49}{3}]$ | $-2e^{4} + \frac{19}{3}e^{3} + 31e^{2} - \frac{248}{3}e - \frac{154}{3}$ |
| 59 | $[59, 59, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - \frac{16}{3}w + \frac{11}{3}]$ | $\phantom{-}\frac{2}{3}e^{4} - \frac{5}{3}e^{3} - \frac{31}{3}e^{2} + \frac{68}{3}e + \frac{32}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{13}{3}]$ | $1$ |