Base field 4.4.13676.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 4, w^{2} - 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 3x^{3} - 11x^{2} - 31x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 1]$ | $\phantom{-}0$ |
4 | $[4, 2, -w^{2} - w + 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{3} - 5w + 1]$ | $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{9}{4}e + \frac{5}{2}$ |
11 | $[11, 11, -w^{3} + 6w - 2]$ | $-e - 1$ |
13 | $[13, 13, -w^{2} + 4]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{13}{4}e + \frac{3}{2}$ |
17 | $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ | $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{13}{4}e - \frac{11}{2}$ |
37 | $[37, 37, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}\frac{3}{4}e^{3} + \frac{3}{2}e^{2} - \frac{31}{4}e - \frac{17}{2}$ |
37 | $[37, 37, -w^{3} + 6w - 4]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{17}{4}e + \frac{1}{2}$ |
41 | $[41, 41, -w^{3} + 5w - 5]$ | $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{9}{4}e - \frac{13}{2}$ |
43 | $[43, 43, w^{3} - 4w + 4]$ | $-e^{3} - e^{2} + 10e + 10$ |
43 | $[43, 43, -2w^{3} + 11w - 2]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e - 1$ |
47 | $[47, 47, -2w^{3} - w^{2} + 12w]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{7}{2}e - 4$ |
47 | $[47, 47, 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{9}{2}e - 9$ |
61 | $[61, 61, -w^{3} + w^{2} + 6w - 5]$ | $\phantom{-}e^{3} + e^{2} - 11e - 9$ |
71 | $[71, 71, w^{3} + w^{2} - 4w - 3]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{13}{2}e + 11$ |
71 | $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ | $\phantom{-}e^{3} + 2e^{2} - 10e - 15$ |
79 | $[79, 79, w^{3} + w^{2} - 6w - 5]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{17}{2}e + 5$ |
81 | $[81, 3, -3]$ | $-\frac{3}{4}e^{3} - \frac{1}{2}e^{2} + \frac{23}{4}e - \frac{5}{2}$ |
83 | $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{11}{2}e + 2$ |
97 | $[97, 97, w^{3} + w^{2} - 6w + 1]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{1}{2}e^{2} - \frac{43}{4}e + \frac{5}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 1]$ | $-1$ |