Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[3, 3, -w - 2]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 3x^{4} - 12x^{3} + 28x^{2} + 35x - 57\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 3]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + 2e^{2} - \frac{3}{2}e - \frac{7}{4}$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{7}{2}e + \frac{15}{2}$ |
| 9 | $[9, 3, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{7}{2}e + \frac{17}{2}$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - 3e^{2} + \frac{7}{2}e + \frac{23}{4}$ |
| 13 | $[13, 13, -w + 2]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{7}{2}e - \frac{11}{2}$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + 3e^{2} - \frac{3}{2}e - \frac{19}{4}$ |
| 23 | $[23, 23, w^{2} - 4w + 1]$ | $-\frac{1}{4}e^{4} + e^{3} + \frac{3}{2}e^{2} - 5e - \frac{9}{4}$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{1}{4}e^{4} + e^{3} + \frac{1}{2}e^{2} - 4e + \frac{35}{4}$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + \frac{3}{2}e - \frac{23}{2}$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{2}e^{2} - 3e + \frac{41}{4}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + 2e^{2} - \frac{7}{2}e + \frac{9}{4}$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + 2e^{2} - \frac{5}{2}e - \frac{15}{4}$ |
| 41 | $[41, 41, w^{2} - w - 10]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 3$ |
| 43 | $[43, 43, -2w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{2}e^{2} - 2e + \frac{41}{4}$ |
| 47 | $[47, 47, -w^{2} - w + 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{7}{2}e^{2} + \frac{13}{2}e$ |
| 49 | $[49, 7, -w^{2} + 5w - 5]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - e^{2} - \frac{1}{2}e - \frac{25}{4}$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{7}{2}e^{2} - \frac{17}{2}e - 6$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - e^{3} - \frac{7}{2}e^{2} + 9e + \frac{33}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 2]$ | $-1$ |