Base field 3.3.1425.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[3, 3, w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 11x^{2} + 5x + 22\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
5 | $[5, 5, w^{2} - w - 7]$ | $-\frac{1}{4}e^{3} + \frac{7}{4}e + \frac{1}{2}$ |
8 | $[8, 2, 2]$ | $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{5}{4}e - \frac{5}{2}$ |
11 | $[11, 11, w - 1]$ | $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{9}{4}e - \frac{7}{2}$ |
13 | $[13, 13, w^{2} - 2w - 8]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{1}{2}e - 8$ |
17 | $[17, 17, w^{2} - 2w - 7]$ | $-\frac{3}{4}e^{3} + \frac{21}{4}e + \frac{3}{2}$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{4}e^{3} - e^{2} - \frac{3}{4}e + \frac{17}{2}$ |
19 | $[19, 19, -2w^{2} + 3w + 16]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{11}{4}e + \frac{1}{2}$ |
23 | $[23, 23, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{4}e^{3} + e^{2} - \frac{15}{4}e - \frac{15}{2}$ |
31 | $[31, 31, 2w^{2} - 3w - 13]$ | $-e^{3} + e^{2} + 6e - 2$ |
37 | $[37, 37, w^{2} - w - 10]$ | $\phantom{-}\frac{1}{4}e^{3} - e^{2} - \frac{11}{4}e + \frac{11}{2}$ |
43 | $[43, 43, 3w^{2} - 5w - 19]$ | $\phantom{-}\frac{3}{4}e^{3} - 2e^{2} - \frac{25}{4}e + \frac{19}{2}$ |
43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e + 1$ |
43 | $[43, 43, 2w^{2} - 2w - 17]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{5}{2}e + 9$ |
47 | $[47, 47, w^{2} - 2]$ | $-\frac{1}{4}e^{3} + \frac{19}{4}e + \frac{3}{2}$ |
67 | $[67, 67, w^{2} - 3w - 5]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{1}{2}e - 5$ |
79 | $[79, 79, -w^{2} + 3w - 1]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e - 1$ |
83 | $[83, 83, w^{2} + w - 4]$ | $\phantom{-}\frac{5}{4}e^{3} - 3e^{2} - \frac{35}{4}e + \frac{29}{2}$ |
97 | $[97, 97, w^{2} - 11]$ | $\phantom{-}\frac{1}{4}e^{3} - 4e^{2} - \frac{7}{4}e + \frac{45}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $-1$ |