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: | $[401, 401, 7w - 25]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 15x^{4} + 12x^{3} + 39x^{2} - 24x - 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -2w + 1]$ | $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + \frac{7}{2}e^{3} + \frac{1}{2}e^{2} - \frac{33}{4}e - \frac{5}{4}$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 6e^{3} - e^{2} - \frac{19}{2}e + \frac{3}{2}$ |
| 11 | $[11, 11, -3w + 2]$ | $\phantom{-}e^{5} + \frac{3}{2}e^{4} - 12e^{3} - 5e^{2} + 22e + \frac{21}{2}$ |
| 11 | $[11, 11, -3w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - 4e^{3} + 5e^{2} + \frac{27}{4}e - \frac{15}{4}$ |
| 19 | $[19, 19, -4w + 3]$ | $-\frac{3}{4}e^{5} - \frac{7}{4}e^{4} + 8e^{3} + 11e^{2} - \frac{61}{4}e - \frac{77}{4}$ |
| 19 | $[19, 19, -4w + 1]$ | $\phantom{-}e^{5} + 2e^{4} - 12e^{3} - 13e^{2} + 25e + 25$ |
| 29 | $[29, 29, w + 5]$ | $\phantom{-}e^{2} + 2e - 5$ |
| 29 | $[29, 29, -w + 6]$ | $-2e^{5} - 4e^{4} + 23e^{3} + 22e^{2} - 47e - 38$ |
| 31 | $[31, 31, -5w + 2]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 7e^{3} + 2e^{2} - \frac{33}{2}e - \frac{15}{2}$ |
| 31 | $[31, 31, -5w + 3]$ | $\phantom{-}\frac{3}{4}e^{5} + \frac{3}{4}e^{4} - 9e^{3} + e^{2} + \frac{49}{4}e + \frac{1}{4}$ |
| 41 | $[41, 41, -6w + 5]$ | $\phantom{-}\frac{3}{2}e^{5} + \frac{5}{2}e^{4} - 18e^{3} - 11e^{2} + \frac{73}{2}e + \frac{41}{2}$ |
| 41 | $[41, 41, w - 7]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{3}{2}e^{4} - 6e^{3} - 14e^{2} + \frac{35}{2}e + \frac{57}{2}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{5}{4}e^{5} + \frac{9}{4}e^{4} - \frac{27}{2}e^{3} - \frac{17}{2}e^{2} + \frac{89}{4}e + \frac{41}{4}$ |
| 59 | $[59, 59, 2w - 9]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{3}{4}e^{4} - 3e^{3} - 8e^{2} + \frac{31}{4}e + \frac{65}{4}$ |
| 59 | $[59, 59, 7w - 5]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 7e^{3} + 3e^{2} - \frac{29}{2}e - \frac{29}{2}$ |
| 61 | $[61, 61, 3w - 10]$ | $-\frac{5}{4}e^{5} - \frac{5}{4}e^{4} + \frac{31}{2}e^{3} - \frac{1}{2}e^{2} - \frac{97}{4}e - \frac{9}{4}$ |
| 61 | $[61, 61, -3w - 7]$ | $-2e^{5} - 4e^{4} + 24e^{3} + 25e^{2} - 52e - 47$ |
| 71 | $[71, 71, -8w + 7]$ | $\phantom{-}e^{4} - 14e^{2} + 8e + 25$ |
| 71 | $[71, 71, w - 9]$ | $-\frac{7}{4}e^{5} - \frac{11}{4}e^{4} + 21e^{3} + 12e^{2} - \frac{157}{4}e - \frac{101}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $401$ | $[401, 401, 7w - 25]$ | $1$ |