Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ |
| 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:
| \(x^{5} + 5x^{4} - 8x^{3} - 61x^{2} - 30x + 75\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 6w^{2} - 2w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - w - 4]$ | $-\frac{2}{5}e^{4} - e^{3} + \frac{26}{5}e^{2} + \frac{47}{5}e - 10$ |
| 11 | $[11, 11, -2w^{4} + w^{3} + 10w^{2} + w - 3]$ | $\phantom{-}\frac{3}{5}e^{4} + e^{3} - \frac{44}{5}e^{2} - \frac{53}{5}e + 19$ |
| 11 | $[11, 11, w^{4} - 6w^{2} - 3w + 3]$ | $\phantom{-}\frac{2}{5}e^{4} + e^{3} - \frac{26}{5}e^{2} - \frac{52}{5}e + 7$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}\frac{3}{5}e^{4} + e^{3} - \frac{39}{5}e^{2} - \frac{53}{5}e + 9$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w]$ | $\phantom{-}e^{2} + e - 8$ |
| 27 | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ | $-\frac{3}{5}e^{4} - e^{3} + \frac{44}{5}e^{2} + \frac{53}{5}e - 20$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ | $-1$ |
| 32 | $[32, 2, -2]$ | $-\frac{4}{5}e^{4} - e^{3} + \frac{57}{5}e^{2} + \frac{49}{5}e - 26$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{6}{5}e^{4} + e^{3} - \frac{83}{5}e^{2} - \frac{51}{5}e + 27$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $\phantom{-}\frac{4}{5}e^{4} + e^{3} - \frac{52}{5}e^{2} - \frac{44}{5}e + 15$ |
| 53 | $[53, 53, -w^{4} + 7w^{2} - 3]$ | $-\frac{3}{5}e^{4} - e^{3} + \frac{39}{5}e^{2} + \frac{58}{5}e - 10$ |
| 53 | $[53, 53, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 2]$ | $-\frac{4}{5}e^{4} - e^{3} + \frac{52}{5}e^{2} + \frac{54}{5}e - 14$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 16w^{2} + 8]$ | $-\frac{1}{5}e^{4} + \frac{8}{5}e^{2} - \frac{4}{5}e + 3$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 4w - 3]$ | $-\frac{6}{5}e^{4} - 2e^{3} + \frac{73}{5}e^{2} + \frac{91}{5}e - 22$ |
| 73 | $[73, 73, 2w^{4} - 12w^{2} - 4w + 5]$ | $-\frac{1}{5}e^{4} + \frac{23}{5}e^{2} + \frac{1}{5}e - 17$ |
| 83 | $[83, 83, w^{4} - 5w^{2} - 3w + 3]$ | $-\frac{2}{5}e^{4} + \frac{31}{5}e^{2} + \frac{7}{5}e - 15$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-\frac{17}{5}e^{4} - 6e^{3} + \frac{221}{5}e^{2} + \frac{292}{5}e - 76$ |
| 103 | $[103, 103, 2w^{3} - 3w^{2} - 7w + 3]$ | $-2e^{4} - 3e^{3} + 25e^{2} + 27e - 34$ |
| 109 | $[109, 109, -3w^{4} + 2w^{3} + 14w^{2} + w - 6]$ | $-\frac{3}{5}e^{4} - e^{3} + \frac{34}{5}e^{2} + \frac{58}{5}e - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ | $1$ |