Base field 3.3.1765.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 11x + 16\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[4, 4, -2w^{2} - w + 20]$ |
Dimension: | $6$ |
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:
\(x^{6} - 21x^{4} + 107x^{2} - 7\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $\phantom{-}0$ |
4 | $[4, 2, -w^{2} - w + 9]$ | $\phantom{-}e$ |
5 | $[5, 5, -2w^{2} - w + 21]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{7}{2}$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}$ |
13 | $[13, 13, -2w^{2} - w + 19]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e$ |
13 | $[13, 13, w^{2} - 9]$ | $-\frac{1}{4}e^{4} + \frac{5}{2}e^{2} + \frac{15}{4}$ |
13 | $[13, 13, 3w^{2} + 2w - 29]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} + \frac{73}{4}e$ |
17 | $[17, 17, -w^{2} - 2w + 7]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{11}{2}e^{3} + \frac{113}{4}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{4}e^{5} - 6e^{3} + \frac{139}{4}e$ |
27 | $[27, 3, -3]$ | $-e^{2} + 7$ |
31 | $[31, 31, -w^{2} + 7]$ | $\phantom{-}\frac{1}{4}e^{5} - 6e^{3} + \frac{139}{4}e$ |
43 | $[43, 43, w^{2} - 13]$ | $\phantom{-}\frac{1}{4}e^{4} - 2e^{2} - \frac{29}{4}$ |
47 | $[47, 47, 2w^{2} + 3w - 11]$ | $-e^{3} + 11e$ |
59 | $[59, 59, w^{2} - 5]$ | $-\frac{1}{2}e^{5} + 10e^{3} - \frac{91}{2}e$ |
61 | $[61, 61, 5w^{2} + 4w - 47]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{35}{2}e$ |
61 | $[61, 61, 4w - 7]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{33}{2}e$ |
61 | $[61, 61, w - 5]$ | $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} + 1$ |
71 | $[71, 71, -2w^{2} - 2w + 21]$ | $\phantom{-}\frac{3}{4}e^{5} - 14e^{3} + \frac{241}{4}e$ |
73 | $[73, 73, -2w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{11}{2}e^{3} + \frac{109}{4}e$ |
79 | $[79, 79, w + 5]$ | $\phantom{-}2e^{2} - 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 2]$ | $-1$ |