Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[10, 10, -w^{3} + 3w^{2} + 2w - 6]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 3x^{4} - 11x^{3} + 19x^{2} + 40x + 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $-1$ |
5 | $[5, 5, w^{2} - 2w - 3]$ | $-1$ |
5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{9}{4}e^{2} + \frac{41}{4}e + \frac{15}{2}$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}e^{2} - 2e - 4$ |
17 | $[17, 17, -w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{5}{2}e^{3} - \frac{5}{2}e^{2} + \frac{31}{2}e + 9$ |
23 | $[23, 23, w^{2} - 3]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{9}{2}e^{2} - \frac{19}{2}e - 9$ |
25 | $[25, 5, -w^{2} + 2w + 1]$ | $\phantom{-}2e - 4$ |
37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $-e^{3} + 2e^{2} + 7e - 4$ |
41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{5}{2}e^{2} + \frac{11}{2}e - 3$ |
49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $\phantom{-}e^{3} - 3e^{2} - 5e + 8$ |
49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 15e + 8$ |
59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}e^{4} - 3e^{3} - 8e^{2} + 15e + 18$ |
67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $\phantom{-}e^{3} - 4e^{2} - 3e + 14$ |
71 | $[71, 71, 2w - 3]$ | $\phantom{-}e^{2} - 6$ |
71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{3} - \frac{5}{2}e^{2} + \frac{51}{2}e + 15$ |
79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $\phantom{-}e^{4} - 3e^{3} - 8e^{2} + 15e + 14$ |
79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{5}{2}e^{2} + \frac{9}{2}e - 1$ |
81 | $[81, 3, -3]$ | $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 14e + 10$ |
83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $\phantom{-}e^{4} - 4e^{3} - 8e^{2} + 26e + 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $1$ |
$5$ | $[5, 5, w^{2} - 2w - 3]$ | $1$ |