Base field 4.4.15125.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 14x^{2} + 14x + 31\); narrow class number \(4\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 28x^{4} + 207x^{2} - 162\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, 4w^{3} + 7w^{2} - 37w - 45]$ | $\phantom{-}e$ |
11 | $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ | $-\frac{1}{27}e^{5} + \frac{19}{27}e^{3} - \frac{10}{3}e$ |
11 | $[11, 11, -w + 2]$ | $\phantom{-}\frac{2}{27}e^{5} - \frac{29}{27}e^{3} + \frac{1}{3}e$ |
16 | $[16, 2, 2]$ | $-\frac{1}{9}e^{4} + \frac{10}{9}e^{2} + 1$ |
19 | $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{3} - w^{2} + 9w + 3]$ | $\phantom{-}\frac{4}{9}e^{4} - \frac{58}{9}e^{2} + 4$ |
19 | $[19, 19, -2w^{3} - 4w^{2} + 17w + 23]$ | $-\frac{1}{27}e^{5} + \frac{19}{27}e^{3} - \frac{10}{3}e$ |
19 | $[19, 19, w^{3} + 2w^{2} - 10w - 10]$ | $-\frac{1}{3}e^{3} + \frac{13}{3}e$ |
29 | $[29, 29, -w - 2]$ | $-\frac{5}{9}e^{4} + \frac{77}{9}e^{2} - 14$ |
29 | $[29, 29, -w^{3} - 2w^{2} + 8w + 15]$ | $-\frac{1}{9}e^{4} + \frac{19}{9}e^{2} - 12$ |
29 | $[29, 29, 2w^{3} + 3w^{2} - 18w - 20]$ | $-\frac{2}{9}e^{5} + \frac{35}{9}e^{3} - \frac{35}{3}e$ |
29 | $[29, 29, -3w^{3} - 5w^{2} + 27w + 28]$ | $\phantom{-}\frac{1}{27}e^{5} - \frac{10}{27}e^{3} - 3e$ |
31 | $[31, 31, 3w^{3} + 5w^{2} - 27w - 31]$ | $-\frac{2}{27}e^{5} + \frac{20}{27}e^{3} + 5e$ |
31 | $[31, 31, -3w^{3} - 5w^{2} + 27w + 30]$ | $\phantom{-}\frac{5}{27}e^{5} - \frac{95}{27}e^{3} + \frac{41}{3}e$ |
31 | $[31, 31, -2w^{3} - 3w^{2} + 18w + 17]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{13}{9}e^{3} - \frac{5}{3}e$ |
31 | $[31, 31, 2w^{3} + 3w^{2} - 18w - 18]$ | $-\frac{2}{27}e^{5} + \frac{29}{27}e^{3} - \frac{4}{3}e$ |
71 | $[71, 71, -w^{3} - 2w^{2} + 10w + 8]$ | $-\frac{2}{9}e^{4} + \frac{11}{9}e^{2} + 14$ |
71 | $[71, 71, 4w^{3} + 8w^{2} - 35w - 50]$ | $-\frac{8}{9}e^{4} + \frac{125}{9}e^{2} - 22$ |
71 | $[71, 71, -4w^{3} - 7w^{2} + 36w + 47]$ | $\phantom{-}\frac{11}{9}e^{4} - \frac{164}{9}e^{2} + 22$ |
71 | $[71, 71, -w^{3} - 2w^{2} + 8w + 17]$ | $-\frac{2}{3}e^{4} + \frac{29}{3}e^{2} - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ | $-1$ |