Base field \(\Q(\sqrt{5}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[331, 331, -17w + 14]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 17x^{4} + 32x^{3} + 39x^{2} - 86x + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -2w + 1]$ | $\phantom{-}\frac{3}{28}e^{5} - \frac{1}{28}e^{4} - \frac{12}{7}e^{3} + \frac{1}{14}e^{2} + \frac{69}{28}e + \frac{11}{28}$ |
| 9 | $[9, 3, 3]$ | $-\frac{11}{28}e^{5} + \frac{3}{14}e^{4} + \frac{95}{14}e^{3} - \frac{17}{7}e^{2} - \frac{463}{28}e + \frac{107}{14}$ |
| 11 | $[11, 11, -3w + 2]$ | $\phantom{-}\frac{3}{14}e^{5} - \frac{9}{28}e^{4} - \frac{55}{14}e^{3} + \frac{65}{14}e^{2} + \frac{80}{7}e - \frac{237}{28}$ |
| 11 | $[11, 11, -3w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} - \frac{1}{2}e^{2} + \frac{45}{4}e - \frac{3}{2}$ |
| 19 | $[19, 19, -4w + 3]$ | $-\frac{3}{7}e^{5} + \frac{1}{7}e^{4} + \frac{55}{7}e^{3} - \frac{9}{7}e^{2} - \frac{160}{7}e + \frac{52}{7}$ |
| 19 | $[19, 19, -4w + 1]$ | $-\frac{13}{28}e^{5} + \frac{9}{28}e^{4} + \frac{111}{14}e^{3} - \frac{29}{7}e^{2} - \frac{509}{28}e + \frac{307}{28}$ |
| 29 | $[29, 29, w + 5]$ | $-\frac{1}{7}e^{5} + \frac{3}{14}e^{4} + \frac{16}{7}e^{3} - \frac{17}{7}e^{2} - \frac{37}{7}e + \frac{23}{14}$ |
| 29 | $[29, 29, -w + 6]$ | $\phantom{-}\frac{9}{14}e^{5} - \frac{13}{28}e^{4} - \frac{79}{7}e^{3} + \frac{83}{14}e^{2} + \frac{417}{14}e - \frac{501}{28}$ |
| 31 | $[31, 31, -5w + 2]$ | $\phantom{-}\frac{9}{14}e^{5} - \frac{13}{28}e^{4} - \frac{79}{7}e^{3} + \frac{83}{14}e^{2} + \frac{417}{14}e - \frac{445}{28}$ |
| 31 | $[31, 31, -5w + 3]$ | $\phantom{-}\frac{1}{14}e^{5} + \frac{1}{7}e^{4} - \frac{8}{7}e^{3} - \frac{23}{7}e^{2} + \frac{23}{14}e + \frac{52}{7}$ |
| 41 | $[41, 41, -6w + 5]$ | $-\frac{5}{28}e^{5} + \frac{1}{7}e^{4} + \frac{47}{14}e^{3} - \frac{9}{7}e^{2} - \frac{325}{28}e + \frac{24}{7}$ |
| 41 | $[41, 41, w - 7]$ | $\phantom{-}\frac{5}{14}e^{5} + \frac{3}{14}e^{4} - \frac{47}{7}e^{3} - \frac{31}{7}e^{2} + \frac{269}{14}e + \frac{23}{14}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{5}{7}e^{5} - \frac{9}{28}e^{4} - \frac{181}{14}e^{3} + \frac{51}{14}e^{2} + \frac{531}{14}e - \frac{489}{28}$ |
| 59 | $[59, 59, 2w - 9]$ | $\phantom{-}\frac{1}{14}e^{5} + \frac{1}{7}e^{4} - \frac{8}{7}e^{3} - \frac{9}{7}e^{2} - \frac{5}{14}e - \frac{32}{7}$ |
| 59 | $[59, 59, 7w - 5]$ | $-\frac{4}{7}e^{5} + \frac{5}{14}e^{4} + \frac{71}{7}e^{3} - \frac{26}{7}e^{2} - \frac{183}{7}e + \frac{127}{14}$ |
| 61 | $[61, 61, 3w - 10]$ | $-\frac{1}{7}e^{5} - \frac{1}{28}e^{4} + \frac{39}{14}e^{3} + \frac{1}{14}e^{2} - \frac{137}{14}e + \frac{123}{28}$ |
| 61 | $[61, 61, -3w - 7]$ | $-\frac{4}{7}e^{5} + \frac{5}{14}e^{4} + \frac{71}{7}e^{3} - \frac{26}{7}e^{2} - \frac{183}{7}e + \frac{155}{14}$ |
| 71 | $[71, 71, -8w + 7]$ | $\phantom{-}\frac{9}{14}e^{5} - \frac{5}{7}e^{4} - \frac{79}{7}e^{3} + \frac{73}{7}e^{2} + \frac{445}{14}e - \frac{176}{7}$ |
| 71 | $[71, 71, w - 9]$ | $-\frac{41}{28}e^{5} + \frac{23}{28}e^{4} + \frac{363}{14}e^{3} - \frac{71}{7}e^{2} - \frac{1937}{28}e + \frac{965}{28}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $331$ | $[331, 331, -17w + 14]$ | $1$ |