Base field 3.3.1593.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[15, 15, w - 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 11x^{5} + 38x^{4} + 28x^{3} - 67x^{2} - 59x + 52\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 2]$ | $-1$ |
5 | $[5, 5, w^{2} - 2w - 4]$ | $-1$ |
7 | $[7, 7, w]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 3]$ | $-e^{2} - 4e$ |
7 | $[7, 7, -w^{2} + 2w + 3]$ | $\phantom{-}e^{3} + 6e^{2} + 6e - 8$ |
8 | $[8, 2, 2]$ | $-\frac{1}{2}e^{4} - \frac{7}{2}e^{3} - \frac{11}{2}e^{2} + \frac{3}{2}e + 3$ |
13 | $[13, 13, w^{2} - 3w - 2]$ | $-\frac{1}{2}e^{4} - \frac{9}{2}e^{3} - \frac{21}{2}e^{2} - \frac{1}{2}e + 8$ |
17 | $[17, 17, w - 2]$ | $-\frac{1}{2}e^{5} - \frac{9}{2}e^{4} - \frac{21}{2}e^{3} + \frac{5}{2}e^{2} + 18e - 6$ |
25 | $[25, 5, -w^{2} - w + 3]$ | $\phantom{-}e^{5} + 8e^{4} + 13e^{3} - 22e^{2} - 36e + 30$ |
29 | $[29, 29, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{7}{2}e^{3} + \frac{9}{2}e^{2} - \frac{7}{2}e$ |
31 | $[31, 31, w^{2} - 5]$ | $-e^{5} - 8e^{4} - 13e^{3} + 20e^{2} + 30e - 28$ |
37 | $[37, 37, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{9}{2}e^{3} + \frac{25}{2}e^{2} + \frac{13}{2}e - 16$ |
41 | $[41, 41, w^{2} - 8]$ | $\phantom{-}\frac{3}{2}e^{5} + \frac{25}{2}e^{4} + \frac{47}{2}e^{3} - \frac{49}{2}e^{2} - 54e + 34$ |
43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{7}{2}e^{3} + \frac{13}{2}e^{2} + \frac{5}{2}e - 2$ |
53 | $[53, 53, 2w^{2} - 5w - 4]$ | $\phantom{-}2e + 6$ |
59 | $[59, 59, w^{2} - 3]$ | $-\frac{1}{2}e^{5} - \frac{5}{2}e^{4} + \frac{9}{2}e^{3} + \frac{57}{2}e^{2} + 7e - 28$ |
59 | $[59, 59, w^{2} - 3w - 5]$ | $-e^{5} - \frac{15}{2}e^{4} - \frac{19}{2}e^{3} + \frac{57}{2}e^{2} + \frac{77}{2}e - 34$ |
61 | $[61, 61, -w^{2} + 2w + 12]$ | $-\frac{1}{2}e^{5} - \frac{11}{2}e^{4} - \frac{39}{2}e^{3} - \frac{39}{2}e^{2} + 13e + 18$ |
67 | $[67, 67, -2w^{2} + 6w + 3]$ | $-e^{5} - \frac{17}{2}e^{4} - \frac{37}{2}e^{3} + \frac{3}{2}e^{2} + \frac{41}{2}e + 2$ |
71 | $[71, 71, w^{2} - w - 11]$ | $\phantom{-}e^{5} + 9e^{4} + 20e^{3} - 9e^{2} - 33e + 20$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 2]$ | $1$ |
$5$ | $[5, 5, w^{2} - 2w - 4]$ | $1$ |