Base field 4.4.5744.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{3} + w^{2} + 4w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 21x^{2} + 96\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{3} + 4w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 1]$ | $-\frac{1}{4}e^{3} + \frac{13}{4}e$ |
7 | $[7, 7, -w^{2} + w + 2]$ | $-\frac{1}{4}e^{3} + \frac{9}{4}e$ |
13 | $[13, 13, -w^{3} + w^{2} + 4w]$ | $-1$ |
13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e$ |
17 | $[17, 17, -w^{2} + 2]$ | $-2e$ |
19 | $[19, 19, -w^{3} + 5w]$ | $-\frac{1}{4}e^{3} + \frac{13}{4}e$ |
31 | $[31, 31, -w^{2} + 2w + 3]$ | $\phantom{-}e^{2} - 14$ |
37 | $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ | $\phantom{-}2e$ |
43 | $[43, 43, -w - 3]$ | $\phantom{-}2e^{2} - 20$ |
53 | $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{21}{4}e$ |
53 | $[53, 53, w^{3} - 6w - 2]$ | $\phantom{-}e^{2} - 6$ |
59 | $[59, 59, 2w^{3} - w^{2} - 10w - 2]$ | $\phantom{-}e^{2}$ |
61 | $[61, 61, 2w^{3} - w^{2} - 10w]$ | $-e^{2} + 10$ |
61 | $[61, 61, 2w^{3} - w^{2} - 8w]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{31}{4}e$ |
71 | $[71, 71, 2w^{3} - 9w - 2]$ | $-\frac{1}{4}e^{3} + \frac{21}{4}e$ |
73 | $[73, 73, -w^{3} - w^{2} + 6w + 3]$ | $\phantom{-}e^{3} - 13e$ |
81 | $[81, 3, -3]$ | $-e^{2} + 16$ |
83 | $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e$ |
101 | $[101, 101, 2w^{3} - 8w - 3]$ | $-\frac{3}{4}e^{3} + \frac{39}{4}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{3} + w^{2} + 4w]$ | $1$ |