Base field 5.5.179024.1
Generator \(w\), with minimal polynomial \(x^{5} - 8x^{3} + 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{4} + w^{3} - 8w^{2} - 6w + 5]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $39$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - x^{9} - 13x^{8} + 10x^{7} + 62x^{6} - 32x^{5} - 131x^{4} + 32x^{3} + 110x^{2} + 2x - 13\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$ | $\phantom{-}\frac{7}{3}e^{9} + e^{8} - \frac{82}{3}e^{7} - 17e^{6} + \frac{311}{3}e^{5} + 83e^{4} - \frac{392}{3}e^{3} - 128e^{2} + \frac{35}{3}e + \frac{52}{3}$ |
| 11 | $[11, 11, 2w^{4} + w^{3} - 16w^{2} - 9w + 9]$ | $-\frac{5}{3}e^{9} - 3e^{8} + \frac{62}{3}e^{7} + 37e^{6} - \frac{244}{3}e^{5} - 146e^{4} + \frac{301}{3}e^{3} + 192e^{2} + \frac{17}{3}e - \frac{77}{3}$ |
| 17 | $[17, 17, w^{4} + w^{3} - 8w^{2} - 6w + 5]$ | $-1$ |
| 29 | $[29, 29, w^{4} - 8w^{2} + 3]$ | $\phantom{-}e^{9} - 11e^{7} - 2e^{6} + 39e^{5} + 12e^{4} - 46e^{3} - 15e^{2} + 4e - 7$ |
| 43 | $[43, 43, 6w^{4} + 3w^{3} - 46w^{2} - 24w + 21]$ | $-\frac{11}{3}e^{9} - 6e^{8} + \frac{137}{3}e^{7} + 74e^{6} - \frac{547}{3}e^{5} - 292e^{4} + \frac{715}{3}e^{3} + 387e^{2} - \frac{49}{3}e - \frac{170}{3}$ |
| 43 | $[43, 43, 2w^{4} + w^{3} - 15w^{2} - 6w + 7]$ | $-6e^{9} - 4e^{8} + 72e^{7} + 58e^{6} - 279e^{5} - 259e^{4} + 355e^{3} + 375e^{2} - 21e - 44$ |
| 47 | $[47, 47, 3w^{4} + w^{3} - 23w^{2} - 9w + 11]$ | $\phantom{-}6e^{9} - 69e^{7} - 14e^{6} + 256e^{5} + 101e^{4} - 311e^{3} - 184e^{2} + 19e + 17$ |
| 47 | $[47, 47, w^{4} + w^{3} - 8w^{2} - 7w + 3]$ | $\phantom{-}6e^{9} + 6e^{8} - 73e^{7} - 81e^{6} + 287e^{5} + 345e^{4} - 373e^{3} - 486e^{2} + 30e + 65$ |
| 49 | $[49, 7, -w^{4} + 8w^{2} + 2w - 5]$ | $\phantom{-}\frac{8}{3}e^{9} + 7e^{8} - \frac{107}{3}e^{7} - 82e^{6} + \frac{448}{3}e^{5} + 311e^{4} - \frac{589}{3}e^{3} - 394e^{2} - \frac{5}{3}e + \frac{122}{3}$ |
| 53 | $[53, 53, -6w^{4} - 3w^{3} + 46w^{2} + 23w - 23]$ | $\phantom{-}\frac{1}{3}e^{9} + 2e^{8} - \frac{16}{3}e^{7} - 22e^{6} + \frac{74}{3}e^{5} + 78e^{4} - \frac{101}{3}e^{3} - 91e^{2} - \frac{10}{3}e + \frac{4}{3}$ |
| 53 | $[53, 53, 2w^{4} + w^{3} - 15w^{2} - 7w + 5]$ | $-\frac{19}{3}e^{9} - e^{8} + \frac{220}{3}e^{7} + 25e^{6} - \frac{824}{3}e^{5} - 140e^{4} + \frac{1031}{3}e^{3} + 231e^{2} - \frac{116}{3}e - \frac{82}{3}$ |
| 59 | $[59, 59, 13w^{4} + 7w^{3} - 101w^{2} - 54w + 55]$ | $\phantom{-}\frac{1}{3}e^{9} - 2e^{8} - \frac{4}{3}e^{7} + 21e^{6} - \frac{16}{3}e^{5} - 73e^{4} + \frac{67}{3}e^{3} + 88e^{2} - \frac{34}{3}e - \frac{38}{3}$ |
| 67 | $[67, 67, 5w^{4} + 3w^{3} - 39w^{2} - 23w + 19]$ | $\phantom{-}\frac{5}{3}e^{9} - e^{8} - \frac{53}{3}e^{7} + 6e^{6} + \frac{175}{3}e^{5} - 3e^{4} - \frac{157}{3}e^{3} - 20e^{2} - \frac{65}{3}e + \frac{14}{3}$ |
| 67 | $[67, 67, 4w^{4} + 2w^{3} - 32w^{2} - 16w + 19]$ | $\phantom{-}\frac{2}{3}e^{9} + 5e^{8} - \frac{32}{3}e^{7} - 58e^{6} + \frac{151}{3}e^{5} + 218e^{4} - \frac{205}{3}e^{3} - 277e^{2} - \frac{53}{3}e + \frac{131}{3}$ |
| 71 | $[71, 71, 4w^{4} + 3w^{3} - 31w^{2} - 22w + 15]$ | $-\frac{10}{3}e^{9} - 8e^{8} + \frac{130}{3}e^{7} + 96e^{6} - \frac{527}{3}e^{5} - 374e^{4} + \frac{644}{3}e^{3} + 491e^{2} + \frac{88}{3}e - \frac{184}{3}$ |
| 71 | $[71, 71, 9w^{4} + 5w^{3} - 70w^{2} - 38w + 39]$ | $\phantom{-}\frac{26}{3}e^{9} + 3e^{8} - \frac{305}{3}e^{7} - 54e^{6} + \frac{1153}{3}e^{5} + 272e^{4} - \frac{1420}{3}e^{3} - 429e^{2} + \frac{64}{3}e + \frac{170}{3}$ |
| 71 | $[71, 71, 4w^{4} + w^{3} - 31w^{2} - 8w + 17]$ | $-\frac{5}{3}e^{9} + 2e^{8} + \frac{53}{3}e^{7} - 18e^{6} - \frac{178}{3}e^{5} + 50e^{4} + \frac{184}{3}e^{3} - 46e^{2} + \frac{8}{3}e + \frac{28}{3}$ |
| 81 | $[81, 3, -5w^{4} - 2w^{3} + 38w^{2} + 17w - 19]$ | $-9e^{9} - 2e^{8} + 105e^{7} + 44e^{6} - 395e^{5} - 238e^{4} + 483e^{3} + 383e^{2} - 17e - 38$ |
| 83 | $[83, 83, -3w^{4} - w^{3} + 24w^{2} + 9w - 13]$ | $-5e^{9} - e^{8} + 59e^{7} + 23e^{6} - 227e^{5} - 127e^{4} + 299e^{3} + 209e^{2} - 56e - 30$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{4} + w^{3} - 8w^{2} - 6w + 5]$ | $1$ |