Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 2x^{3} - 17x^{2} - 21x + 70\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w + 2]$ | $\phantom{-}1$ |
4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $-1$ |
9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ | $-e$ |
9 | $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ | $\phantom{-}e$ |
11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ | $\phantom{-}e^{3} - e^{2} - 11e + 14$ |
11 | $[11, 11, -w - 3]$ | $-e^{3} + e^{2} + 11e - 16$ |
25 | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $-e^{3} + 2e^{2} + 12e - 24$ |
29 | $[29, 29, w + 1]$ | $-e^{3} + 3e^{2} + 13e - 30$ |
29 | $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ | $-e^{3} + e^{2} + 11e - 20$ |
31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ | $-e + 4$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ | $\phantom{-}e^{3} - e^{2} - 12e + 14$ |
31 | $[31, 31, -w + 3]$ | $\phantom{-}e^{3} - 3e^{2} - 12e + 34$ |
31 | $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ | $-2e^{2} - e + 14$ |
59 | $[59, 59, 2w^{2} - w - 13]$ | $-2e^{3} + 4e^{2} + 24e - 50$ |
59 | $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ | $\phantom{-}2e$ |
61 | $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ | $\phantom{-}2e^{3} - 4e^{2} - 26e + 44$ |
61 | $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ | $-6$ |
71 | $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ | $-e^{3} + 2e^{2} + 15e - 26$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ | $\phantom{-}3e^{3} - 4e^{2} - 35e + 54$ |
79 | $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ | $\phantom{-}e^{3} - 2e^{2} - 12e + 20$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, w + 2]$ | $-1$ |
$4$ | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $1$ |