Base field 4.4.7053.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[39, 39, -w^{3} + 3w^{2} + 2w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 14x^{2} + 16x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{2} - 2w - 1]$ | $\phantom{-}\frac{2}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e + \frac{8}{5}$ |
| 13 | $[13, 13, w^{3} - 3w^{2} - w + 5]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w^{3} - 3w^{2} - w + 2]$ | $-\frac{2}{5}e^{3} - \frac{3}{5}e^{2} + \frac{21}{5}e + \frac{12}{5}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{9}{10}e^{3} + \frac{8}{5}e^{2} - \frac{46}{5}e + \frac{3}{5}$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{3}{10}e^{3} - \frac{6}{5}e^{2} + \frac{7}{5}e + \frac{24}{5}$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 2w - 1]$ | $-\frac{7}{10}e^{3} - \frac{4}{5}e^{2} + \frac{38}{5}e - \frac{4}{5}$ |
| 29 | $[29, 29, -2w^{3} + 5w^{2} + 4w - 7]$ | $\phantom{-}2$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{2}{5}e^{3} - \frac{8}{5}e^{2} + \frac{16}{5}e + \frac{42}{5}$ |
| 47 | $[47, 47, -w^{3} + 4w^{2} - w - 5]$ | $-e^{3} - e^{2} + 12e - 4$ |
| 53 | $[53, 53, -w^{3} + 4w^{2} - w - 7]$ | $\phantom{-}\frac{7}{10}e^{3} + \frac{4}{5}e^{2} - \frac{38}{5}e + \frac{24}{5}$ |
| 67 | $[67, 67, 2w^{3} - 3w^{2} - 8w + 1]$ | $\phantom{-}\frac{6}{5}e^{3} + \frac{4}{5}e^{2} - \frac{78}{5}e + \frac{44}{5}$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 4w + 4]$ | $\phantom{-}\frac{1}{10}e^{3} + \frac{2}{5}e^{2} - \frac{4}{5}e + \frac{2}{5}$ |
| 71 | $[71, 71, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{1}{5}e^{3} + \frac{1}{5}e^{2} + \frac{3}{5}e - \frac{14}{5}$ |
| 79 | $[79, 79, w^{2} - 3w - 4]$ | $-\frac{1}{5}e^{3} + \frac{6}{5}e^{2} + \frac{18}{5}e - \frac{64}{5}$ |
| 83 | $[83, 83, 2w^{2} - 3w - 4]$ | $\phantom{-}\frac{9}{5}e^{3} + \frac{11}{5}e^{2} - \frac{92}{5}e + \frac{16}{5}$ |
| 89 | $[89, 89, -3w^{3} + 7w^{2} + 8w - 11]$ | $\phantom{-}e^{3} + 2e^{2} - 9e - 2$ |
| 101 | $[101, 101, w^{3} - 2w^{2} - 3w - 2]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{4}{5}e^{2} - \frac{12}{5}e + \frac{66}{5}$ |
| 103 | $[103, 103, -2w^{3} + 4w^{2} + 5w - 1]$ | $-\frac{3}{10}e^{3} - \frac{6}{5}e^{2} + \frac{12}{5}e + \frac{64}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |
| $13$ | $[13, 13, w^{3} - 3w^{2} - w + 5]$ | $-1$ |