Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[13, 13, -w + 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 8x^{3} + 6x^{2} + 40x - 31\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w - 2]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{3}{5}e^{2} - \frac{1}{10}e + \frac{9}{5}$ |
5 | $[5, 5, w + 1]$ | $-\frac{1}{5}e^{3} + \frac{6}{5}e^{2} + \frac{1}{5}e - \frac{18}{5}$ |
7 | $[7, 7, w - 3]$ | $\phantom{-}1$ |
8 | $[8, 2, 2]$ | $-\frac{1}{10}e^{3} + \frac{3}{5}e^{2} + \frac{11}{10}e - \frac{9}{5}$ |
9 | $[9, 3, w^{2} - 3w - 2]$ | $-\frac{1}{10}e^{3} + \frac{11}{10}e^{2} - \frac{19}{10}e - \frac{43}{10}$ |
13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{6}{5}e^{2} - \frac{11}{5}e + \frac{38}{5}$ |
13 | $[13, 13, -w + 2]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $-\frac{1}{5}e^{3} + \frac{6}{5}e^{2} + \frac{1}{5}e - \frac{18}{5}$ |
23 | $[23, 23, w^{2} - 4w + 1]$ | $-\frac{1}{10}e^{3} + \frac{3}{5}e^{2} + \frac{11}{10}e - \frac{39}{5}$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{1}{20}e^{3} + \frac{1}{20}e^{2} + \frac{21}{20}e + \frac{7}{20}$ |
31 | $[31, 31, w^{2} - 2w - 9]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{1}{10}e^{2} - \frac{21}{10}e - \frac{7}{10}$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $-\frac{1}{10}e^{3} + \frac{1}{10}e^{2} + \frac{21}{10}e + \frac{7}{10}$ |
41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}e^{2} - 4e - 5$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-e^{2} + 4e + 5$ |
41 | $[41, 41, w^{2} - w - 10]$ | $-\frac{1}{5}e^{3} + \frac{6}{5}e^{2} + \frac{11}{5}e - \frac{38}{5}$ |
43 | $[43, 43, -2w - 3]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{12}{5}e^{2} - \frac{2}{5}e + \frac{36}{5}$ |
47 | $[47, 47, -w^{2} - w + 4]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{3}{5}e^{2} - \frac{11}{10}e + \frac{49}{5}$ |
49 | $[49, 7, -w^{2} + 5w - 5]$ | $-\frac{1}{10}e^{3} + \frac{3}{5}e^{2} + \frac{11}{10}e + \frac{21}{5}$ |
59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{11}{10}e^{2} + \frac{19}{10}e + \frac{43}{10}$ |
59 | $[59, 59, w^{2} - 3]$ | $-\frac{1}{4}e^{3} + \frac{7}{4}e^{2} - \frac{3}{4}e - \frac{23}{4}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w + 2]$ | $-1$ |