Base field 4.4.8069.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, -w^{2} - w + 1]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 7x^{4} + 5x^{3} - 52x^{2} - 101x - 25\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w^{3} - 4w]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{2}{5}e^{4} + \frac{7}{5}e^{3} - \frac{17}{5}e^{2} - \frac{52}{5}e + 1$ |
7 | $[7, 7, -w^{3} + 4w - 1]$ | $\phantom{-}e^{4} + 4e^{3} - 7e^{2} - 32e - 10$ |
13 | $[13, 13, -w^{2} + 3]$ | $-\frac{6}{5}e^{4} - \frac{26}{5}e^{3} + \frac{36}{5}e^{2} + \frac{201}{5}e + 15$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{2}{5}e^{4} + \frac{7}{5}e^{3} - \frac{12}{5}e^{2} - \frac{52}{5}e - 10$ |
17 | $[17, 17, w^{3} + w^{2} - 4w - 2]$ | $-\frac{1}{5}e^{4} - \frac{6}{5}e^{3} + \frac{6}{5}e^{2} + \frac{51}{5}e$ |
17 | $[17, 17, -w^{3} + 5w - 2]$ | $\phantom{-}\frac{3}{5}e^{4} + \frac{13}{5}e^{3} - \frac{18}{5}e^{2} - \frac{103}{5}e - 7$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}\frac{1}{5}e^{4} + \frac{6}{5}e^{3} - \frac{1}{5}e^{2} - \frac{51}{5}e - 9$ |
19 | $[19, 19, -w^{2} - w + 1]$ | $\phantom{-}1$ |
29 | $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ | $-\frac{1}{5}e^{4} - \frac{1}{5}e^{3} + \frac{11}{5}e^{2} + \frac{6}{5}e - 6$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w - 3]$ | $-\frac{11}{5}e^{4} - \frac{41}{5}e^{3} + \frac{81}{5}e^{2} + \frac{311}{5}e + 8$ |
43 | $[43, 43, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}e^{3} + 2e^{2} - 8e - 8$ |
43 | $[43, 43, w^{3} - 6w]$ | $\phantom{-}\frac{7}{5}e^{4} + \frac{27}{5}e^{3} - \frac{52}{5}e^{2} - \frac{222}{5}e - 11$ |
47 | $[47, 47, -w^{3} - w^{2} + 5w]$ | $\phantom{-}\frac{6}{5}e^{4} + \frac{26}{5}e^{3} - \frac{46}{5}e^{2} - \frac{206}{5}e$ |
49 | $[49, 7, w^{2} + 2w - 2]$ | $\phantom{-}\frac{6}{5}e^{4} + \frac{26}{5}e^{3} - \frac{36}{5}e^{2} - \frac{191}{5}e - 17$ |
59 | $[59, 59, 2w^{3} - 8w + 3]$ | $-\frac{14}{5}e^{4} - \frac{59}{5}e^{3} + \frac{89}{5}e^{2} + \frac{454}{5}e + 29$ |
67 | $[67, 67, w^{2} - w - 4]$ | $\phantom{-}2e^{4} + 8e^{3} - 13e^{2} - 65e - 29$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}2e^{4} + 8e^{3} - 15e^{2} - 64e - 8$ |
81 | $[81, 3, -3]$ | $-\frac{7}{5}e^{4} - \frac{32}{5}e^{3} + \frac{42}{5}e^{2} + \frac{252}{5}e + 14$ |
97 | $[97, 97, w^{3} + w^{2} - 5w + 1]$ | $-\frac{12}{5}e^{4} - \frac{47}{5}e^{3} + \frac{82}{5}e^{2} + \frac{372}{5}e + 19$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, -w^{2} - w + 1]$ | $-1$ |