Base field 3.3.1369.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[27, 3, 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $47$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 36x^{3} + 104x^{2} + 131x - 261\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{15}{352}e^{4} - \frac{9}{176}e^{3} - \frac{251}{176}e^{2} + \frac{293}{176}e + \frac{1119}{352}$ |
| 11 | $[11, 11, -w^{2} + 3w + 7]$ | $\phantom{-}\frac{15}{352}e^{4} - \frac{9}{176}e^{3} - \frac{251}{176}e^{2} + \frac{293}{176}e + \frac{1119}{352}$ |
| 11 | $[11, 11, w^{2} - 2w - 8]$ | $\phantom{-}\frac{15}{352}e^{4} - \frac{9}{176}e^{3} - \frac{251}{176}e^{2} + \frac{293}{176}e + \frac{1119}{352}$ |
| 23 | $[23, 23, w^{2} - 2w - 7]$ | $-\frac{13}{352}e^{4} - \frac{1}{176}e^{3} + \frac{285}{176}e^{2} - \frac{75}{176}e - \frac{3909}{352}$ |
| 23 | $[23, 23, w^{2} - 3w - 8]$ | $-\frac{13}{352}e^{4} - \frac{1}{176}e^{3} + \frac{285}{176}e^{2} - \frac{75}{176}e - \frac{3909}{352}$ |
| 23 | $[23, 23, w - 1]$ | $-\frac{13}{352}e^{4} - \frac{1}{176}e^{3} + \frac{285}{176}e^{2} - \frac{75}{176}e - \frac{3909}{352}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{22}e^{4} + \frac{1}{22}e^{3} - \frac{16}{11}e^{2} - \frac{13}{22}e + \frac{57}{22}$ |
| 29 | $[29, 29, w^{2} - 3w - 10]$ | $\phantom{-}\frac{1}{22}e^{4} + \frac{1}{22}e^{3} - \frac{16}{11}e^{2} - \frac{13}{22}e + \frac{57}{22}$ |
| 29 | $[29, 29, w - 3]$ | $\phantom{-}\frac{1}{22}e^{4} + \frac{1}{22}e^{3} - \frac{16}{11}e^{2} - \frac{13}{22}e + \frac{57}{22}$ |
| 31 | $[31, 31, w^{2} - 2w - 6]$ | $\phantom{-}\frac{7}{176}e^{4} - \frac{13}{88}e^{3} - \frac{123}{88}e^{2} + \frac{345}{88}e + \frac{487}{176}$ |
| 31 | $[31, 31, -w^{2} + 3w + 9]$ | $\phantom{-}\frac{7}{176}e^{4} - \frac{13}{88}e^{3} - \frac{123}{88}e^{2} + \frac{345}{88}e + \frac{487}{176}$ |
| 31 | $[31, 31, w - 2]$ | $\phantom{-}\frac{7}{176}e^{4} - \frac{13}{88}e^{3} - \frac{123}{88}e^{2} + \frac{345}{88}e + \frac{487}{176}$ |
| 37 | $[37, 37, -w^{2} + 4w + 7]$ | $-\frac{5}{176}e^{4} + \frac{3}{88}e^{3} + \frac{69}{88}e^{2} + \frac{49}{88}e + \frac{595}{176}$ |
| 43 | $[43, 43, 2w^{2} - 6w - 13]$ | $-\frac{25}{352}e^{4} + \frac{15}{176}e^{3} + \frac{389}{176}e^{2} - \frac{547}{176}e - \frac{985}{352}$ |
| 43 | $[43, 43, 2w^{2} - 4w - 17]$ | $-\frac{25}{352}e^{4} + \frac{15}{176}e^{3} + \frac{389}{176}e^{2} - \frac{547}{176}e - \frac{985}{352}$ |
| 43 | $[43, 43, w^{2} - 2w - 12]$ | $-\frac{25}{352}e^{4} + \frac{15}{176}e^{3} + \frac{389}{176}e^{2} - \frac{547}{176}e - \frac{985}{352}$ |
| 47 | $[47, 47, w^{2} - 4w - 4]$ | $\phantom{-}\frac{3}{176}e^{4} - \frac{15}{88}e^{3} - \frac{37}{88}e^{2} + \frac{327}{88}e - \frac{489}{176}$ |
| 47 | $[47, 47, w^{2} - w - 5]$ | $\phantom{-}\frac{3}{176}e^{4} - \frac{15}{88}e^{3} - \frac{37}{88}e^{2} + \frac{327}{88}e - \frac{489}{176}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, 3]$ | $-1$ |