Base field 3.3.1300.1
Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[16, 4, -2w - 4]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 4x^{4} - 9x^{3} + 38x^{2} + 18x - 76\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
5 | $[5, 5, -w^{2} + 2w + 5]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}e^{2} - e - 6$ |
11 | $[11, 11, -2w^{2} + 5w + 9]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 3e + 8$ |
13 | $[13, 13, -w^{2} + w + 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{3}{4}e^{3} - 2e^{2} + \frac{9}{2}e + 5$ |
13 | $[13, 13, w - 3]$ | $-e^{2} + 2e + 6$ |
17 | $[17, 17, -w^{2} + 2w + 7]$ | $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{5}{2}e^{2} - \frac{1}{2}e - 3$ |
17 | $[17, 17, -2w^{2} + 5w + 7]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{11}{2}e^{2} - 6e - 12$ |
17 | $[17, 17, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 2e + 8$ |
19 | $[19, 19, -w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - 2e + 14$ |
27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 7e^{2} - 3e - 18$ |
31 | $[31, 31, w^{2} - 2w - 9]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 6e^{2} + 2e + 16$ |
37 | $[37, 37, w^{2} - 7]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{5}{4}e^{3} - 10e^{2} + \frac{17}{2}e + 25$ |
41 | $[41, 41, w^{2} - w - 11]$ | $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{3}{2}e^{2} + \frac{1}{2}e + 3$ |
47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 10$ |
49 | $[49, 7, w^{2} - 3w - 1]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{4}e^{3} + e^{2} + \frac{21}{2}e - 7$ |
59 | $[59, 59, w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 7e^{2} - e + 26$ |
67 | $[67, 67, w^{2} - 3w - 7]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{11}{2}e^{2} - 6e - 14$ |
71 | $[71, 71, 4w + 9]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 8e^{2} + 28$ |
73 | $[73, 73, -4w^{2} + 8w + 23]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{3}{2}e^{2} + \frac{17}{2}e - 5$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 2]$ | $-1$ |