Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[31, 31, w^{2} - 2w - 8]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 4x^{3} - 48x^{2} + 104x + 172\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{30}e^{3} - \frac{1}{10}e^{2} - \frac{6}{5}e + \frac{19}{15}$ |
| 8 | $[8, 2, 2]$ | $-1$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $-\frac{1}{30}e^{3} + \frac{1}{10}e^{2} + \frac{11}{5}e - \frac{19}{15}$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}\frac{1}{60}e^{3} - \frac{2}{15}e^{2} - \frac{13}{30}e + \frac{14}{5}$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{1}{60}e^{3} - \frac{2}{15}e^{2} - \frac{13}{30}e + \frac{14}{5}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{1}{30}e^{3} + \frac{1}{10}e^{2} + \frac{6}{5}e - \frac{19}{15}$ |
| 17 | $[17, 17, -w^{2} + w + 8]$ | $-\frac{1}{30}e^{3} + \frac{1}{10}e^{2} + \frac{11}{5}e - \frac{79}{15}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{7}{30}e^{2} - \frac{49}{30}e + \frac{61}{15}$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $-\frac{1}{20}e^{3} + \frac{1}{15}e^{2} + \frac{59}{30}e + \frac{4}{15}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - \frac{26}{3}$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{1}{30}e^{3} - \frac{1}{10}e^{2} - \frac{6}{5}e + \frac{19}{15}$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}8$ |
| 31 | $[31, 31, w^{2} - 2w - 8]$ | $\phantom{-}1$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $-\frac{1}{30}e^{3} + \frac{1}{10}e^{2} + \frac{11}{5}e - \frac{79}{15}$ |
| 41 | $[41, 41, -w - 4]$ | $\phantom{-}\frac{1}{30}e^{3} - \frac{1}{10}e^{2} - \frac{11}{5}e + \frac{79}{15}$ |
| 41 | $[41, 41, w^{2} - 2w - 7]$ | $\phantom{-}\frac{1}{30}e^{3} - \frac{1}{10}e^{2} - \frac{11}{5}e + \frac{79}{15}$ |
| 47 | $[47, 47, 2w^{2} - 3w - 7]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{7}{2}e - \frac{10}{3}$ |
| 53 | $[53, 53, -w^{2} + w + 9]$ | $-\frac{1}{30}e^{3} + \frac{1}{10}e^{2} + \frac{11}{5}e + \frac{11}{15}$ |
| 61 | $[61, 61, 3w^{2} - 2w - 17]$ | $-\frac{1}{60}e^{3} - \frac{11}{30}e^{2} + \frac{43}{30}e + \frac{51}{5}$ |
| 67 | $[67, 67, 2w - 1]$ | $-\frac{1}{30}e^{3} - \frac{2}{5}e^{2} + \frac{11}{5}e + \frac{176}{15}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, w^{2} - 2w - 8]$ | $-1$ |