Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, w - 1]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 2x^{8} - 13x^{7} + 22x^{6} + 58x^{5} - 75x^{4} - 106x^{3} + 95x^{2} + 66x - 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $-\frac{1}{18}e^{8} - \frac{2}{9}e^{7} + \frac{25}{18}e^{6} + \frac{19}{9}e^{5} - \frac{77}{9}e^{4} - \frac{31}{6}e^{3} + \frac{125}{9}e^{2} + \frac{55}{18}e - \frac{10}{3}$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{1}{9}e^{8} + \frac{5}{9}e^{7} + \frac{7}{9}e^{6} - \frac{52}{9}e^{5} - \frac{1}{9}e^{4} + \frac{50}{3}e^{3} - \frac{38}{9}e^{2} - \frac{107}{9}e + \frac{13}{3}$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $-\frac{1}{3}e^{8} + \frac{2}{3}e^{7} + \frac{10}{3}e^{6} - \frac{16}{3}e^{5} - \frac{28}{3}e^{4} + 8e^{3} + \frac{22}{3}e^{2} + \frac{4}{3}e + 1$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{4}{9}e^{8} - \frac{11}{9}e^{7} - \frac{37}{9}e^{6} + \frac{100}{9}e^{5} + \frac{85}{9}e^{4} - \frac{77}{3}e^{3} - \frac{19}{9}e^{2} + \frac{140}{9}e - \frac{19}{3}$ |
| 13 | $[13, 13, -2w + 1]$ | $-\frac{4}{9}e^{8} + \frac{11}{9}e^{7} + \frac{37}{9}e^{6} - \frac{100}{9}e^{5} - \frac{85}{9}e^{4} + \frac{74}{3}e^{3} + \frac{28}{9}e^{2} - \frac{113}{9}e + \frac{16}{3}$ |
| 19 | $[19, 19, 2w^{2} - w - 15]$ | $-\frac{5}{9}e^{8} + \frac{16}{9}e^{7} + \frac{44}{9}e^{6} - \frac{161}{9}e^{5} - \frac{86}{9}e^{4} + \frac{151}{3}e^{3} - \frac{1}{9}e^{2} - \frac{364}{9}e + \frac{26}{3}$ |
| 25 | $[25, 5, w^{2} - 7]$ | $-\frac{1}{9}e^{8} - \frac{4}{9}e^{7} + \frac{25}{9}e^{6} + \frac{38}{9}e^{5} - \frac{163}{9}e^{4} - \frac{34}{3}e^{3} + \frac{331}{9}e^{2} + \frac{100}{9}e - \frac{50}{3}$ |
| 27 | $[27, 3, 3]$ | $-\frac{2}{3}e^{8} + \frac{7}{3}e^{7} + \frac{17}{3}e^{6} - \frac{68}{3}e^{5} - \frac{29}{3}e^{4} + 59e^{3} - \frac{22}{3}e^{2} - \frac{124}{3}e + 18$ |
| 31 | $[31, 31, w^{2} - 2w - 1]$ | $\phantom{-}\frac{1}{9}e^{8} - \frac{5}{9}e^{7} - \frac{7}{9}e^{6} + \frac{52}{9}e^{5} + \frac{1}{9}e^{4} - \frac{53}{3}e^{3} + \frac{47}{9}e^{2} + \frac{170}{9}e - \frac{16}{3}$ |
| 37 | $[37, 37, -3w^{2} + 2w + 23]$ | $\phantom{-}\frac{4}{9}e^{8} - \frac{11}{9}e^{7} - \frac{37}{9}e^{6} + \frac{100}{9}e^{5} + \frac{94}{9}e^{4} - \frac{74}{3}e^{3} - \frac{91}{9}e^{2} + \frac{77}{9}e + \frac{8}{3}$ |
| 41 | $[41, 41, -2w - 1]$ | $\phantom{-}\frac{1}{3}e^{8} - \frac{2}{3}e^{7} - \frac{13}{3}e^{6} + \frac{19}{3}e^{5} + \frac{58}{3}e^{4} - 15e^{3} - \frac{100}{3}e^{2} + \frac{20}{3}e + 14$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{1}{3}e^{8} - \frac{2}{3}e^{7} - \frac{13}{3}e^{6} + \frac{19}{3}e^{5} + \frac{58}{3}e^{4} - 15e^{3} - \frac{100}{3}e^{2} + \frac{26}{3}e + 14$ |
| 49 | $[49, 7, w^{2} - 2w - 5]$ | $\phantom{-}\frac{8}{9}e^{8} - \frac{13}{9}e^{7} - \frac{92}{9}e^{6} + \frac{110}{9}e^{5} + \frac{332}{9}e^{4} - \frac{67}{3}e^{3} - \frac{434}{9}e^{2} + \frac{46}{9}e + \frac{58}{3}$ |
| 59 | $[59, 59, 2w - 3]$ | $\phantom{-}\frac{2}{3}e^{8} - \frac{7}{3}e^{7} - \frac{14}{3}e^{6} + \frac{65}{3}e^{5} + \frac{5}{3}e^{4} - 53e^{3} + \frac{55}{3}e^{2} + \frac{109}{3}e - 14$ |
| 67 | $[67, 67, w - 5]$ | $-\frac{7}{9}e^{8} + \frac{26}{9}e^{7} + \frac{49}{9}e^{6} - \frac{247}{9}e^{5} - \frac{7}{9}e^{4} + \frac{209}{3}e^{3} - \frac{284}{9}e^{2} - \frac{452}{9}e + \frac{91}{3}$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $\phantom{-}\frac{1}{3}e^{8} - \frac{5}{3}e^{7} - \frac{4}{3}e^{6} + \frac{49}{3}e^{5} - \frac{26}{3}e^{4} - 43e^{3} + \frac{101}{3}e^{2} + \frac{83}{3}e - 28$ |
| 73 | $[73, 73, w^{2} + 1]$ | $-\frac{1}{9}e^{8} + \frac{14}{9}e^{7} - \frac{20}{9}e^{6} - \frac{151}{9}e^{5} + \frac{251}{9}e^{4} + \frac{167}{3}e^{3} - \frac{632}{9}e^{2} - \frac{530}{9}e + \frac{130}{3}$ |
| 83 | $[83, 83, -4w^{2} + 3w + 27]$ | $\phantom{-}\frac{2}{3}e^{8} - \frac{4}{3}e^{7} - \frac{23}{3}e^{6} + \frac{41}{3}e^{5} + \frac{80}{3}e^{4} - 39e^{3} - \frac{86}{3}e^{2} + \frac{82}{3}e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w - 1]$ | $-1$ |