Base field 4.4.8768.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[28, 14, -w^{3} + 3w^{2} + w - 4]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 4x^{3} - 13x^{2} + 34x + 71\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{2} + w + 3]$ | $-1$ |
7 | $[7, 7, w]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $-1$ |
7 | $[7, 7, w^{2} - 2]$ | $\phantom{-}e^{3} - \frac{5}{2}e^{2} - \frac{15}{2}e + \frac{7}{2}$ |
7 | $[7, 7, w - 1]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + \frac{13}{2}$ |
23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{1}{2}e^{3} - e^{2} + 9e + \frac{35}{2}$ |
23 | $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{19}{2}e - 21$ |
31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}\frac{9}{2}e^{2} - \frac{19}{2}e - \frac{75}{2}$ |
31 | $[31, 31, -w^{2} + 2w + 4]$ | $-e^{3} + \frac{3}{2}e^{2} + \frac{17}{2}e + \frac{15}{2}$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ | $-e^{2} + e + 9$ |
41 | $[41, 41, w^{3} - w^{2} - 3w - 3]$ | $\phantom{-}e^{3} - 3e^{2} - 6e + 14$ |
47 | $[47, 47, w^{2} - 2w - 5]$ | $-\frac{1}{2}e^{3} + \frac{13}{2}e^{2} - \frac{17}{2}e - 45$ |
47 | $[47, 47, w^{2} - 6]$ | $-\frac{1}{2}e^{3} + 2e^{2} + 3e - \frac{3}{2}$ |
71 | $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ | $-2e^{3} + 3e^{2} + 19e + 11$ |
71 | $[71, 71, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}e^{3} - 7e^{2} + 3e + 44$ |
79 | $[79, 79, -w - 3]$ | $-\frac{1}{2}e^{3} + \frac{23}{2}e^{2} - \frac{35}{2}e - 89$ |
79 | $[79, 79, w - 4]$ | $\phantom{-}e^{3} - 7e^{2} + 2e + 39$ |
81 | $[81, 3, -3]$ | $-\frac{1}{2}e^{3} + e^{2} + 3e - \frac{9}{2}$ |
89 | $[89, 89, w^{2} - 3w - 2]$ | $-\frac{1}{2}e^{3} + e^{2} + 4e + \frac{15}{2}$ |
89 | $[89, 89, w^{2} + w - 4]$ | $\phantom{-}3e^{3} - 12e^{2} - 13e + 52$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{2} + w + 3]$ | $1$ |
$7$ | $[7, 7, -w^{2} + 2w + 1]$ | $1$ |