Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 2x^{6} - 15x^{5} + 30x^{4} + 54x^{3} - 108x^{2} - 19x + 56\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $-\frac{1}{6}e^{6} + \frac{5}{2}e^{4} - \frac{1}{2}e^{3} - \frac{19}{2}e^{2} + 3e + \frac{17}{3}$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{1}{3}e^{6} + \frac{1}{2}e^{5} + \frac{11}{2}e^{4} - 6e^{3} - \frac{47}{2}e^{2} + 13e + \frac{52}{3}$ |
| 29 | $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ | $-\frac{1}{3}e^{6} + \frac{1}{2}e^{5} + 5e^{4} - \frac{13}{2}e^{3} - \frac{37}{2}e^{2} + \frac{35}{2}e + \frac{31}{3}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1}{6}e^{6} - 2e^{4} + \frac{7}{2}e^{2} + \frac{1}{2}e + \frac{13}{3}$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{1}{3}e^{6} + 5e^{4} - 19e^{2} + \frac{37}{3}$ |
| 41 | $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ | $\phantom{-}\frac{1}{3}e^{6} - 5e^{4} + 20e^{2} + 2e - \frac{49}{3}$ |
| 43 | $[43, 43, -2w^{4} + 3w^{3} + 8w^{2} - 8w - 6]$ | $-\frac{1}{3}e^{6} + 5e^{4} - e^{3} - 19e^{2} + 6e + \frac{40}{3}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 5w^{2} + 6w + 5]$ | $\phantom{-}\frac{1}{3}e^{6} - 5e^{4} + e^{3} + 19e^{2} - 6e - \frac{34}{3}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ | $-e^{3} - e^{2} + 6e + 5$ |
| 61 | $[61, 61, w^{2} - 2w - 3]$ | $\phantom{-}e^{3} + e^{2} - 8e - 1$ |
| 67 | $[67, 67, w^{4} - w^{3} - 4w^{2} + 3w]$ | $-\frac{1}{3}e^{6} + 6e^{4} - 29e^{2} - e + \frac{76}{3}$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{1}{2}e^{5} - 5e^{4} + \frac{15}{2}e^{3} + \frac{35}{2}e^{2} - \frac{47}{2}e - \frac{34}{3}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 5]$ | $-2e^{2} + 14$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 5w + 3]$ | $-e^{4} + 10e^{2} - 12$ |
| 71 | $[71, 71, 2w^{4} - 2w^{3} - 8w^{2} + 5w + 4]$ | $\phantom{-}\frac{1}{3}e^{6} - 6e^{4} + 29e^{2} - e - \frac{82}{3}$ |
| 73 | $[73, 73, -2w^{4} + 2w^{3} + 9w^{2} - 5w - 6]$ | $\phantom{-}\frac{1}{3}e^{6} - 5e^{4} + 20e^{2} + 2e - \frac{43}{3}$ |
| 81 | $[81, 3, -2w^{4} + 3w^{3} + 10w^{2} - 9w - 10]$ | $-e^{3} + e^{2} + 8e - 7$ |
| 97 | $[97, 97, -2w^{4} + 3w^{3} + 7w^{2} - 5w - 4]$ | $\phantom{-}\frac{1}{3}e^{6} - 5e^{4} + 20e^{2} - \frac{37}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ | $-1$ |