Base field 3.3.1129.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[11, 11, -w^{2} + 5]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 3x^{5} - 9x^{4} - 28x^{3} + 15x^{2} + 63x + 26\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{1}{3}e^{3} - \frac{7}{3}e^{2} - \frac{4}{3}e + \frac{1}{3}$ |
3 | $[3, 3, w + 2]$ | $-\frac{1}{3}e^{5} - \frac{2}{3}e^{4} + 3e^{3} + \frac{14}{3}e^{2} - 6e - \frac{19}{3}$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} - \frac{1}{3}e^{2} - \frac{19}{3}e - \frac{23}{3}$ |
11 | $[11, 11, -w^{2} + 5]$ | $-1$ |
13 | $[13, 13, w^{2} - w - 7]$ | $-\frac{1}{3}e^{5} - e^{4} + \frac{5}{3}e^{3} + 6e^{2} - \frac{2}{3}e - \frac{20}{3}$ |
17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{5}{3}e^{3} - \frac{11}{3}e^{2} - \frac{26}{3}e - \frac{1}{3}$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{4}{3}e^{4} - \frac{7}{3}e^{3} - \frac{28}{3}e^{2} + \frac{10}{3}e + 11$ |
29 | $[29, 29, 2w^{2} - 2w - 11]$ | $\phantom{-}\frac{1}{3}e^{5} + e^{4} - \frac{5}{3}e^{3} - 6e^{2} - \frac{1}{3}e + \frac{5}{3}$ |
31 | $[31, 31, w^{2} - 2w - 4]$ | $-e^{2} + 4$ |
37 | $[37, 37, -2w^{2} + 3w + 7]$ | $-\frac{1}{3}e^{5} - \frac{2}{3}e^{4} + 4e^{3} + \frac{17}{3}e^{2} - 12e - \frac{34}{3}$ |
41 | $[41, 41, w^{2} - 2]$ | $-e^{4} - 2e^{3} + 5e^{2} + 8e$ |
59 | $[59, 59, 2w^{2} - 13]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - 3e^{3} - \frac{17}{3}e^{2} + 6e + \frac{40}{3}$ |
61 | $[61, 61, w^{2} + w - 10]$ | $\phantom{-}e^{5} + \frac{5}{3}e^{4} - \frac{31}{3}e^{3} - \frac{41}{3}e^{2} + \frac{82}{3}e + \frac{86}{3}$ |
67 | $[67, 67, 2w^{2} - w - 11]$ | $\phantom{-}\frac{1}{3}e^{5} + e^{4} - \frac{2}{3}e^{3} - 4e^{2} - \frac{22}{3}e + \frac{2}{3}$ |
73 | $[73, 73, -w^{2} - 1]$ | $-e^{5} - \frac{7}{3}e^{4} + \frac{23}{3}e^{3} + \frac{37}{3}e^{2} - \frac{41}{3}e - \frac{19}{3}$ |
83 | $[83, 83, w^{2} - w - 10]$ | $-\frac{2}{3}e^{5} - 2e^{4} + \frac{16}{3}e^{3} + 12e^{2} - \frac{31}{3}e - \frac{25}{3}$ |
89 | $[89, 89, -w^{2} + 4w - 2]$ | $\phantom{-}e^{5} + \frac{1}{3}e^{4} - \frac{38}{3}e^{3} - \frac{13}{3}e^{2} + \frac{110}{3}e + \frac{52}{3}$ |
97 | $[97, 97, w^{2} - 2w - 7]$ | $\phantom{-}\frac{5}{3}e^{4} + \frac{11}{3}e^{3} - \frac{29}{3}e^{2} - \frac{50}{3}e - \frac{4}{3}$ |
97 | $[97, 97, -w^{2} - 4w - 5]$ | $-e^{5} - \frac{4}{3}e^{4} + \frac{35}{3}e^{3} + \frac{31}{3}e^{2} - \frac{110}{3}e - \frac{76}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11, 11, -w^{2} + 5]$ | $1$ |