Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7, 7, -w^{2} + 2w + 1]$ |
Dimension: | $6$ |
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:
\(x^{6} - 12x^{4} + 31x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 11e$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $-1$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e^{2} - 4$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}2$ |
16 | $[16, 2, 2]$ | $\phantom{-}1$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 13e$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-e^{3} + 7e$ |
25 | $[25, 5, w^{2} - w - 3]$ | $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} - 8$ |
37 | $[37, 37, 2w - 1]$ | $-e^{2} + 2$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 6$ |
43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $-e^{4} + 10e^{2} - 12$ |
59 | $[59, 59, 2w - 5]$ | $\phantom{-}e^{5} - 11e^{3} + 22e$ |
59 | $[59, 59, -2w - 3]$ | $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 16e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$ |
79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $-e^{4} + 10e^{2} - 8$ |
83 | $[83, 83, -w^{3} + 7w]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 16e$ |
83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}e^{5} - 14e^{3} + 46e$ |
83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $-e^{5} + 11e^{3} - 22e$ |
83 | $[83, 83, w^{2} - 2w - 6]$ | $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - 24e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w^{2} + 2w + 1]$ | $1$ |