Base field 4.4.3981.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 4x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[37, 37, w^{3} - w^{2} - 5w + 1]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 4x^{5} - 5x^{4} + 30x^{3} - 10x^{2} - 24x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{3}{2}e^{4} - 3e^{3} + 10e^{2} - 3e - 2$ |
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{7}{4}e^{4} + \frac{27}{2}e^{2} - 11e - 8$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 4e^{2} - 2e - 3$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{7}{4}e^{4} - \frac{11}{2}e^{3} + \frac{21}{2}e^{2} + 3e + 2$ |
| 23 | $[23, 23, w^{2} - 2w - 2]$ | $\phantom{-}e^{3} - e^{2} - 7e + 4$ |
| 37 | $[37, 37, w^{3} - 4w + 1]$ | $-\frac{1}{2}e^{5} + \frac{3}{2}e^{4} + 4e^{3} - 9e^{2} - 5e - 2$ |
| 37 | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $-1$ |
| 41 | $[41, 41, w^{3} - 5w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - 4e^{3} - \frac{1}{2}e^{2} + 12e - 5$ |
| 43 | $[43, 43, 2w^{3} - w^{2} - 7w]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{3}{4}e^{4} - 2e^{3} + \frac{11}{2}e^{2} + 5e$ |
| 53 | $[53, 53, 2w - 3]$ | $-\frac{3}{4}e^{5} + \frac{1}{4}e^{4} + 9e^{3} - \frac{1}{2}e^{2} - 22e - 7$ |
| 59 | $[59, 59, -2w^{3} + w^{2} + 9w - 1]$ | $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{7}{2}e^{3} + \frac{13}{2}e^{2} - 10e - 8$ |
| 67 | $[67, 67, -w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{5}{4}e^{4} - 5e^{3} - \frac{23}{2}e^{2} + 19e + 15$ |
| 67 | $[67, 67, w^{3} + w^{2} - 5w - 4]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{5}{2}e^{3} + \frac{1}{2}e^{2} + 7e$ |
| 71 | $[71, 71, 2w^{3} - 3w^{2} - 7w + 5]$ | $\phantom{-}\frac{1}{2}e^{5} + e^{4} - \frac{19}{2}e^{3} - 10e^{2} + 39e + 11$ |
| 73 | $[73, 73, w^{3} - 6w]$ | $-\frac{9}{4}e^{5} + \frac{25}{4}e^{4} + \frac{31}{2}e^{3} - \frac{85}{2}e^{2} - 2e + 18$ |
| 73 | $[73, 73, -w^{3} - w^{2} + 5w + 3]$ | $-\frac{3}{4}e^{5} + \frac{17}{4}e^{4} - \frac{61}{2}e^{2} + 31e + 23$ |
| 79 | $[79, 79, w^{3} - 3w - 4]$ | $-\frac{1}{4}e^{5} + \frac{3}{4}e^{4} + e^{3} - \frac{5}{2}e^{2} + 3e - 6$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 3w + 1]$ | $-e^{4} + 3e^{3} + 9e^{2} - 20e - 11$ |
| 83 | $[83, 83, -2w^{3} + 2w^{2} + 6w - 3]$ | $-e^{5} + 3e^{4} + 6e^{3} - 21e^{2} + 4e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $1$ |