Base field 3.3.1425.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, w - 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 5x^{6} - 2x^{5} - 37x^{4} - 23x^{3} + 64x^{2} + 41x - 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{2}{13}e^{6} - \frac{2}{13}e^{5} + \frac{25}{13}e^{4} + e^{3} - \frac{84}{13}e^{2} - e + \frac{35}{13}$ |
| 5 | $[5, 5, w^{2} - w - 7]$ | $\phantom{-}e + 1$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{13}e^{6} + \frac{1}{13}e^{5} - \frac{6}{13}e^{4} - \frac{10}{13}e^{2} - 2e + \frac{41}{13}$ |
| 11 | $[11, 11, w - 1]$ | $-1$ |
| 13 | $[13, 13, w^{2} - 2w - 8]$ | $-\frac{6}{13}e^{6} - \frac{19}{13}e^{5} + \frac{36}{13}e^{4} + 9e^{3} - \frac{31}{13}e^{2} - 9e - \frac{51}{13}$ |
| 17 | $[17, 17, w^{2} - 2w - 7]$ | $-\frac{1}{13}e^{6} - \frac{1}{13}e^{5} + \frac{6}{13}e^{4} - e^{3} - \frac{16}{13}e^{2} + 6e + \frac{24}{13}$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{4}{13}e^{6} + \frac{4}{13}e^{5} - \frac{50}{13}e^{4} - 2e^{3} + \frac{168}{13}e^{2} + e - \frac{109}{13}$ |
| 19 | $[19, 19, -2w^{2} + 3w + 16]$ | $-\frac{9}{13}e^{6} - \frac{22}{13}e^{5} + \frac{80}{13}e^{4} + 12e^{3} - \frac{183}{13}e^{2} - 16e + \frac{47}{13}$ |
| 23 | $[23, 23, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{13}e^{6} + \frac{1}{13}e^{5} - \frac{19}{13}e^{4} - e^{3} + \frac{94}{13}e^{2} + 2e - \frac{89}{13}$ |
| 31 | $[31, 31, 2w^{2} - 3w - 13]$ | $\phantom{-}\frac{6}{13}e^{6} + \frac{19}{13}e^{5} - \frac{36}{13}e^{4} - 10e^{3} + \frac{5}{13}e^{2} + 12e + \frac{64}{13}$ |
| 37 | $[37, 37, w^{2} - w - 10]$ | $\phantom{-}\frac{10}{13}e^{6} + \frac{36}{13}e^{5} - \frac{60}{13}e^{4} - 18e^{3} + \frac{82}{13}e^{2} + 20e - \frac{84}{13}$ |
| 43 | $[43, 43, 3w^{2} - 5w - 19]$ | $-\frac{4}{13}e^{6} - \frac{17}{13}e^{5} + \frac{24}{13}e^{4} + 10e^{3} - \frac{25}{13}e^{2} - 14e + \frac{44}{13}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{5}{13}e^{6} - \frac{18}{13}e^{5} + \frac{30}{13}e^{4} + 10e^{3} - \frac{28}{13}e^{2} - 16e + \frac{3}{13}$ |
| 43 | $[43, 43, 2w^{2} - 2w - 17]$ | $-\frac{1}{13}e^{6} - \frac{1}{13}e^{5} + \frac{19}{13}e^{4} + 2e^{3} - \frac{81}{13}e^{2} - 8e + \frac{76}{13}$ |
| 47 | $[47, 47, w^{2} - 2]$ | $-\frac{14}{13}e^{6} - \frac{40}{13}e^{5} + \frac{110}{13}e^{4} + 22e^{3} - \frac{237}{13}e^{2} - 33e + \frac{102}{13}$ |
| 67 | $[67, 67, w^{2} - 3w - 5]$ | $-e^{3} + 4e - 5$ |
| 79 | $[79, 79, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{10}{13}e^{6} + \frac{23}{13}e^{5} - \frac{86}{13}e^{4} - 11e^{3} + \frac{212}{13}e^{2} + 8e - \frac{227}{13}$ |
| 83 | $[83, 83, w^{2} + w - 4]$ | $\phantom{-}\frac{5}{13}e^{6} + \frac{5}{13}e^{5} - \frac{43}{13}e^{4} - e^{3} + \frac{67}{13}e^{2} - 5e + \frac{36}{13}$ |
| 97 | $[97, 97, w^{2} - 11]$ | $\phantom{-}\frac{21}{13}e^{6} + \frac{60}{13}e^{5} - \frac{165}{13}e^{4} - 32e^{3} + \frac{362}{13}e^{2} + 42e - \frac{309}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w - 1]$ | $1$ |