Base field 4.4.9225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 10x^{2} + 7x + 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 4, \frac{1}{4}w^{3} - \frac{5}{2}w - \frac{3}{4}]$ |
Dimension: | $4$ |
CM: | yes |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 4x^{3} - 13x^{2} + 64x - 44\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ | $\phantom{-}0$ |
4 | $[4, 2, \frac{1}{2}w^{3} - 4w - \frac{1}{2}]$ | $\phantom{-}e$ |
9 | $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ | $\phantom{-}0$ |
11 | $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{7}{4}]$ | $\phantom{-}0$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{3}{2}]$ | $\phantom{-}0$ |
19 | $[19, 19, w]$ | $-\frac{3}{2}e^{3} + \frac{43}{2}e - 10$ |
19 | $[19, 19, \frac{1}{4}w^{3} - \frac{5}{2}w + \frac{1}{4}]$ | $\phantom{-}2e^{3} - e^{2} - 30e + 29$ |
25 | $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ | $\phantom{-}e^{3} - e^{2} - 13e + 19$ |
29 | $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ | $\phantom{-}0$ |
29 | $[29, 29, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{9}{2}]$ | $\phantom{-}0$ |
41 | $[41, 41, -w^{3} + 7w + 3]$ | $\phantom{-}0$ |
41 | $[41, 41, -\frac{3}{4}w^{3} + \frac{11}{2}w - \frac{3}{4}]$ | $\phantom{-}0$ |
41 | $[41, 41, \frac{1}{4}w^{3} + w^{2} - \frac{5}{2}w - \frac{11}{4}]$ | $\phantom{-}0$ |
71 | $[71, 71, \frac{1}{2}w^{3} - 4w + \frac{5}{2}]$ | $\phantom{-}0$ |
71 | $[71, 71, \frac{3}{4}w^{3} + w^{2} - \frac{11}{2}w - \frac{21}{4}]$ | $\phantom{-}0$ |
79 | $[79, 79, \frac{1}{4}w^{3} - 2w^{2} + \frac{1}{2}w + \frac{25}{4}]$ | $\phantom{-}e^{3} - e^{2} - 17e + 17$ |
79 | $[79, 79, -\frac{3}{4}w^{3} + \frac{13}{2}w + \frac{9}{4}]$ | $-\frac{7}{2}e^{3} + \frac{103}{2}e - 26$ |
89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{41}{4}]$ | $\phantom{-}0$ |
89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{33}{4}]$ | $\phantom{-}0$ |
101 | $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{1}{2}w - \frac{27}{4}]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ | $1$ |