Base field 4.4.8112.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 13x^{2} + 24\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
4 | $[4, 2, w^{2} - w - 1]$ | $-e$ |
9 | $[9, 3, -w^{2} + 2]$ | $-e^{2} + 8$ |
13 | $[13, 13, w^{3} - 4w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$ |
13 | $[13, 13, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$ |
17 | $[17, 17, w^{3} - 3w - 1]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e$ |
17 | $[17, 17, -w^{3} + 3w - 1]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e$ |
29 | $[29, 29, w^{3} + w^{2} - 4w - 2]$ | $-\frac{1}{2}e^{3} + \frac{13}{2}e$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 2]$ | $-\frac{1}{2}e^{3} + \frac{13}{2}e$ |
43 | $[43, 43, w^{2} + w - 4]$ | $\phantom{-}e^{2} - 8$ |
43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}e^{2} - 8$ |
53 | $[53, 53, w^{3} - 2w - 2]$ | $\phantom{-}0$ |
53 | $[53, 53, -w^{3} + 2w - 2]$ | $\phantom{-}0$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $-e^{3} + 9e$ |
79 | $[79, 79, -w^{3} - w^{2} + 4w + 1]$ | $-e^{3} + 9e$ |
101 | $[101, 101, -w^{3} + w^{2} + 3w - 5]$ | $-6$ |
101 | $[101, 101, w^{3} + w^{2} - 3w - 5]$ | $-6$ |
103 | $[103, 103, 2w^{2} - w - 4]$ | $-4$ |
103 | $[103, 103, 2w^{2} + w - 4]$ | $-4$ |
107 | $[107, 107, 2w^{2} + w - 5]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).