Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[21, 21, w^{2} - 2w - 6]$ |
Dimension: | $3$ |
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:
\(x^{3} + 2x^{2} - 32x - 80\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
7 | $[7, 7, w - 1]$ | $\phantom{-}1$ |
8 | $[8, 2, 2]$ | $-1$ |
9 | $[9, 3, -w^{2} + 2w + 4]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{4}e^{2} - e - 8$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{1}{4}e^{2} + 4$ |
19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{1}{4}e^{2} - e - 10$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{4}e^{2} - e - 10$ |
19 | $[19, 19, -w^{2} + 3w + 2]$ | $-\frac{1}{2}e^{2} + 10$ |
23 | $[23, 23, w^{2} - w - 3]$ | $-\frac{1}{4}e^{2} + e + 4$ |
23 | $[23, 23, -w^{2} + 2]$ | $-6$ |
23 | $[23, 23, -w + 4]$ | $\phantom{-}\frac{1}{4}e^{2} + e - 6$ |
31 | $[31, 31, w^{2} - 5]$ | $-\frac{1}{2}e^{2} + 12$ |
43 | $[43, 43, w^{2} - 3w - 3]$ | $-6$ |
49 | $[49, 7, w^{2} - 6]$ | $\phantom{-}\frac{3}{4}e^{2} - e - 20$ |
53 | $[53, 53, 2w - 5]$ | $-\frac{1}{2}e^{2} + 14$ |
61 | $[61, 61, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{3}{4}e^{2} - 18$ |
71 | $[71, 71, 2w - 3]$ | $-\frac{1}{2}e^{2} + 12$ |
73 | $[73, 73, 2w^{2} - 5w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 16$ |
83 | $[83, 83, w^{2} - w - 9]$ | $-e^{2} + 2e + 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $-1$ |
$7$ | $[7, 7, w - 1]$ | $-1$ |