Base field 5.5.38569.1
Generator \(w\), with minimal polynomial \(x^{5} - 5x^{3} + 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[73, 73, w^{4} - 3w^{2} - w - 1]$ |
| 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:
| \(x^{5} - 10x^{4} + 30x^{3} - 15x^{2} - 53x + 52\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{4}{7}e^{4} - \frac{30}{7}e^{3} + \frac{45}{7}e^{2} + 7e - \frac{72}{7}$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $-\frac{3}{7}e^{4} + \frac{26}{7}e^{3} - \frac{53}{7}e^{2} - 5e + \frac{124}{7}$ |
| 13 | $[13, 13, w^{4} - 5w^{2} + 2]$ | $\phantom{-}e^{4} - 7e^{3} + 9e^{2} + 12e - 14$ |
| 17 | $[17, 17, w^{3} - 3w - 1]$ | $-\frac{5}{7}e^{4} + \frac{34}{7}e^{3} - \frac{37}{7}e^{2} - 11e + \frac{90}{7}$ |
| 32 | $[32, 2, 2]$ | $-\frac{11}{7}e^{4} + \frac{86}{7}e^{3} - \frac{143}{7}e^{2} - 20e + \frac{275}{7}$ |
| 37 | $[37, 37, w^{4} + w^{3} - 5w^{2} - 5w + 4]$ | $\phantom{-}\frac{9}{7}e^{4} - \frac{78}{7}e^{3} + \frac{166}{7}e^{2} + 11e - \frac{302}{7}$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{6}{7}e^{4} + \frac{45}{7}e^{3} - \frac{64}{7}e^{2} - 11e + \frac{80}{7}$ |
| 43 | $[43, 43, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-\frac{11}{7}e^{4} + \frac{86}{7}e^{3} - \frac{150}{7}e^{2} - 16e + \frac{296}{7}$ |
| 47 | $[47, 47, -w^{4} - w^{3} + 6w^{2} + 4w - 5]$ | $-\frac{6}{7}e^{4} + \frac{52}{7}e^{3} - \frac{113}{7}e^{2} - 6e + \frac{192}{7}$ |
| 59 | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ | $\phantom{-}\frac{1}{7}e^{4} - \frac{11}{7}e^{3} + \frac{41}{7}e^{2} - 5e - \frac{88}{7}$ |
| 67 | $[67, 67, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{4}{7}e^{4} + \frac{30}{7}e^{3} - \frac{59}{7}e^{2} - 3e + \frac{128}{7}$ |
| 73 | $[73, 73, w^{4} - 3w^{2} - w - 1]$ | $\phantom{-}1$ |
| 73 | $[73, 73, -2w^{4} - w^{3} + 9w^{2} + 5w - 6]$ | $-\frac{5}{7}e^{4} + \frac{27}{7}e^{3} - \frac{2}{7}e^{2} - 10e - \frac{22}{7}$ |
| 79 | $[79, 79, -3w^{4} + 13w^{2} + 2w - 7]$ | $-\frac{3}{7}e^{4} + \frac{26}{7}e^{3} - \frac{67}{7}e^{2} + 3e + \frac{124}{7}$ |
| 79 | $[79, 79, -w^{3} + 5w]$ | $\phantom{-}\frac{13}{7}e^{4} - \frac{94}{7}e^{3} + \frac{134}{7}e^{2} + 23e - \frac{276}{7}$ |
| 79 | $[79, 79, -w^{4} + 3w^{2} + 1]$ | $\phantom{-}\frac{13}{7}e^{4} - \frac{94}{7}e^{3} + \frac{127}{7}e^{2} + 26e - \frac{220}{7}$ |
| 83 | $[83, 83, -2w^{4} - 2w^{3} + 11w^{2} + 7w - 8]$ | $-\frac{4}{7}e^{4} + \frac{23}{7}e^{3} - \frac{17}{7}e^{2} - 2e - \frac{12}{7}$ |
| 89 | $[89, 89, -w^{4} - 2w^{3} + 4w^{2} + 7w - 3]$ | $-3e^{4} + 23e^{3} - 38e^{2} - 39e + 82$ |
| 101 | $[101, 101, -w^{4} + 5w^{2} - w - 4]$ | $-\frac{12}{7}e^{4} + \frac{97}{7}e^{3} - \frac{177}{7}e^{2} - 24e + \frac{426}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $73$ | $[73, 73, w^{4} - 3w^{2} - w - 1]$ | $-1$ |