Base field 5.5.36497.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 3x^{3} + 5x^{2} + x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[67, 67, -w^{4} + 3w^{3} + w^{2} - 7w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 6x^{3} - 2x^{2} + 43x - 41\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $\phantom{-}\frac{4}{37}e^{3} - \frac{17}{37}e^{2} - \frac{47}{37}e + \frac{136}{37}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}e$ |
| 23 | $[23, 23, 2w^{4} - 3w^{3} - 6w^{2} + 5w + 1]$ | $-\frac{23}{37}e^{3} + \frac{107}{37}e^{2} + \frac{150}{37}e - \frac{597}{37}$ |
| 25 | $[25, 5, -w^{2} + 2w + 2]$ | $-\frac{25}{37}e^{3} + \frac{97}{37}e^{2} + \frac{192}{37}e - \frac{406}{37}$ |
| 29 | $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-\frac{18}{37}e^{3} + \frac{58}{37}e^{2} + \frac{193}{37}e - \frac{242}{37}$ |
| 31 | $[31, 31, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{37}e^{3} + \frac{5}{37}e^{2} - \frac{21}{37}e + \frac{108}{37}$ |
| 32 | $[32, 2, 2]$ | $-\frac{3}{37}e^{3} + \frac{22}{37}e^{2} + \frac{26}{37}e - \frac{250}{37}$ |
| 37 | $[37, 37, w^{4} - 2w^{3} - 2w^{2} + 4w + 1]$ | $\phantom{-}\frac{10}{37}e^{3} - \frac{61}{37}e^{2} - \frac{25}{37}e + \frac{451}{37}$ |
| 47 | $[47, 47, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ | $\phantom{-}\frac{5}{37}e^{3} - \frac{49}{37}e^{2} + \frac{6}{37}e + \frac{392}{37}$ |
| 47 | $[47, 47, 2w^{4} - 3w^{3} - 6w^{2} + 6w + 2]$ | $-\frac{32}{37}e^{3} + \frac{99}{37}e^{2} + \frac{376}{37}e - \frac{644}{37}$ |
| 49 | $[49, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $-\frac{7}{37}e^{3} + \frac{76}{37}e^{2} - \frac{38}{37}e - \frac{423}{37}$ |
| 53 | $[53, 53, -2w^{4} + 3w^{3} + 7w^{2} - 7w - 2]$ | $\phantom{-}\frac{22}{37}e^{3} - \frac{75}{37}e^{2} - \frac{277}{37}e + \frac{600}{37}$ |
| 59 | $[59, 59, -2w^{4} + 3w^{3} + 6w^{2} - 5w - 2]$ | $\phantom{-}\frac{8}{37}e^{3} - \frac{71}{37}e^{2} + \frac{54}{37}e + \frac{457}{37}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 7w]$ | $\phantom{-}\frac{22}{37}e^{3} - \frac{112}{37}e^{2} - \frac{240}{37}e + \frac{933}{37}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + w^{2} - 7w + 1]$ | $\phantom{-}1$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 4w^{2} + 3w + 3]$ | $\phantom{-}\frac{4}{37}e^{3} - \frac{17}{37}e^{2} + \frac{27}{37}e - \frac{12}{37}$ |
| 71 | $[71, 71, -w^{2} + 5]$ | $\phantom{-}e^{3} - 4e^{2} - 8e + 28$ |
| 79 | $[79, 79, 2w^{4} - 3w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}\frac{66}{37}e^{3} - \frac{262}{37}e^{2} - \frac{535}{37}e + \frac{1467}{37}$ |
| 81 | $[81, 3, -w^{4} + 3w^{3} + 3w^{2} - 8w - 2]$ | $\phantom{-}\frac{15}{37}e^{3} - \frac{73}{37}e^{2} - \frac{130}{37}e + \frac{695}{37}$ |
| 83 | $[83, 83, -3w^{4} + 3w^{3} + 10w^{2} - 2w - 2]$ | $\phantom{-}\frac{28}{37}e^{3} - \frac{156}{37}e^{2} - \frac{218}{37}e + \frac{989}{37}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $67$ | $[67, 67, -w^{4} + 3w^{3} + w^{2} - 7w + 1]$ | $-1$ |