Base field 3.3.985.1
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: | $[7, 7, -w + 2]$ |
Dimension: | $5$ |
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:
\(x^{5} + 4x^{4} - 11x^{3} - 38x^{2} + 28x + 24\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 1]$ | $-\frac{1}{8}e^{4} - \frac{1}{4}e^{3} + \frac{11}{8}e^{2} + \frac{3}{2}e - \frac{5}{2}$ |
7 | $[7, 7, -w + 2]$ | $-1$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{1}{4}e^{3} - \frac{15}{8}e^{2} - 3e + \frac{9}{2}$ |
11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{9}{2}e - 3$ |
17 | $[17, 17, -w - 3]$ | $\phantom{-}e - 2$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
17 | $[17, 17, -w^{2} + w + 4]$ | $-4$ |
23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e - 5$ |
27 | $[27, 3, -3]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{1}{4}e^{3} - \frac{15}{8}e^{2} + \frac{9}{2}e + \frac{5}{2}$ |
29 | $[29, 29, w^{2} - w - 8]$ | $-\frac{1}{4}e^{4} - \frac{3}{2}e^{3} + \frac{7}{4}e^{2} + 12e - 3$ |
29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{13}{4}e^{2} - \frac{5}{2}e + 6$ |
29 | $[29, 29, w^{2} - w - 1]$ | $-\frac{1}{8}e^{4} - \frac{3}{4}e^{3} - \frac{1}{8}e^{2} + \frac{9}{2}e + \frac{11}{2}$ |
31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e + 5$ |
37 | $[37, 37, 2w - 5]$ | $\phantom{-}\frac{1}{4}e^{4} + e^{3} - \frac{13}{4}e^{2} - 10e + 5$ |
43 | $[43, 43, w^{2} - 2w - 5]$ | $-\frac{1}{8}e^{4} + \frac{1}{4}e^{3} + \frac{15}{8}e^{2} - \frac{5}{2}e + \frac{3}{2}$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{11}{2}e^{2} + 4e - 10$ |
49 | $[49, 7, w^{2} + w - 4]$ | $-\frac{1}{8}e^{4} - \frac{3}{4}e^{3} + \frac{3}{8}e^{2} + 4e - \frac{3}{2}$ |
53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{7}{4}e^{2} - 2e - 9$ |
71 | $[71, 71, w - 5]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{3}{4}e^{3} + \frac{1}{8}e^{2} - \frac{9}{2}e - \frac{11}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w + 2]$ | $1$ |