Base field \(\Q(\sqrt{119}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 119\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 6x^{3} - 13x^{2} + 66x + 61\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 11]$ | $\phantom{-}0$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e + \frac{105}{43}$ |
5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e + \frac{105}{43}$ |
7 | $[7, 7, w]$ | $\phantom{-}0$ |
9 | $[9, 3, 3]$ | $-\frac{6}{43}e^{3} + \frac{27}{43}e^{2} + \frac{54}{43}e - \frac{229}{43}$ |
11 | $[11, 11, w + 3]$ | $-\frac{2}{43}e^{3} + \frac{9}{43}e^{2} + \frac{61}{43}e - \frac{105}{43}$ |
11 | $[11, 11, w + 8]$ | $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{61}{43}e + \frac{105}{43}$ |
17 | $[17, 17, w]$ | $-\frac{8}{43}e^{3} + \frac{36}{43}e^{2} + \frac{72}{43}e - \frac{162}{43}$ |
19 | $[19, 19, w - 10]$ | $-\frac{1}{43}e^{3} + \frac{26}{43}e^{2} - \frac{34}{43}e - \frac{289}{43}$ |
19 | $[19, 19, -w - 10]$ | $\phantom{-}\frac{1}{43}e^{3} - \frac{26}{43}e^{2} + \frac{34}{43}e + \frac{289}{43}$ |
23 | $[23, 23, w + 2]$ | $-\frac{1}{43}e^{3} + \frac{26}{43}e^{2} - \frac{34}{43}e - \frac{289}{43}$ |
23 | $[23, 23, w + 21]$ | $\phantom{-}\frac{1}{43}e^{3} - \frac{26}{43}e^{2} + \frac{34}{43}e + \frac{289}{43}$ |
41 | $[41, 41, w + 18]$ | $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e - \frac{24}{43}$ |
41 | $[41, 41, w + 23]$ | $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{18}{43}e - \frac{24}{43}$ |
47 | $[47, 47, -3w + 32]$ | $\phantom{-}\frac{2}{43}e^{3} - \frac{9}{43}e^{2} - \frac{61}{43}e + \frac{105}{43}$ |
47 | $[47, 47, 8w - 87]$ | $-\frac{2}{43}e^{3} + \frac{9}{43}e^{2} + \frac{61}{43}e - \frac{105}{43}$ |
53 | $[53, 53, -2w + 23]$ | $-\frac{6}{43}e^{3} + \frac{27}{43}e^{2} + \frac{54}{43}e - \frac{57}{43}$ |
53 | $[53, 53, -13w + 142]$ | $-\frac{6}{43}e^{3} + \frac{27}{43}e^{2} + \frac{54}{43}e - \frac{57}{43}$ |
59 | $[59, 59, -5w + 54]$ | $-\frac{4}{43}e^{3} + \frac{18}{43}e^{2} + \frac{122}{43}e - \frac{210}{43}$ |
59 | $[59, 59, 6w - 65]$ | $\phantom{-}\frac{4}{43}e^{3} - \frac{18}{43}e^{2} - \frac{122}{43}e + \frac{210}{43}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 11]$ | $-1$ |