Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[16, 4, 4]$ |
Dimension: | $5$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 21x^{3} - 17x^{2} + 96x + 120\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 6]$ | $\phantom{-}0$ |
2 | $[2, 2, w + 5]$ | $\phantom{-}0$ |
7 | $[7, 7, 6w - 35]$ | $\phantom{-}e$ |
7 | $[7, 7, -6w - 29]$ | $\phantom{-}e$ |
9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{17}{2}e^{2} - \frac{15}{2}e - 30$ |
11 | $[11, 11, 4w + 19]$ | $-e^{2} + e + 8$ |
11 | $[11, 11, 4w - 23]$ | $-e^{2} + e + 8$ |
13 | $[13, 13, -2w + 11]$ | $-\frac{1}{6}e^{4} + \frac{2}{3}e^{3} + \frac{11}{6}e^{2} - \frac{11}{2}e - 6$ |
13 | $[13, 13, 2w + 9]$ | $-\frac{1}{6}e^{4} + \frac{2}{3}e^{3} + \frac{11}{6}e^{2} - \frac{11}{2}e - 6$ |
25 | $[25, 5, -5]$ | $-\frac{1}{3}e^{4} + \frac{1}{3}e^{3} + \frac{17}{3}e^{2} - 2e - 14$ |
31 | $[31, 31, 2w - 13]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{17}{3}e^{2} + e + 20$ |
31 | $[31, 31, -2w - 11]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{17}{3}e^{2} + e + 20$ |
41 | $[41, 41, -8w - 39]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{15}{2}e^{2} - \frac{13}{2}e - 26$ |
41 | $[41, 41, 8w - 47]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{15}{2}e^{2} - \frac{13}{2}e - 26$ |
53 | $[53, 53, -26w - 125]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{19}{2}e^{2} - \frac{17}{2}e - 42$ |
53 | $[53, 53, 26w - 151]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{19}{2}e^{2} - \frac{17}{2}e - 42$ |
61 | $[61, 61, -14w + 81]$ | $\phantom{-}\frac{2}{3}e^{4} - \frac{5}{3}e^{3} - \frac{31}{3}e^{2} + 12e + 40$ |
61 | $[61, 61, -14w - 67]$ | $\phantom{-}\frac{2}{3}e^{4} - \frac{5}{3}e^{3} - \frac{31}{3}e^{2} + 12e + 40$ |
83 | $[83, 83, 2w - 15]$ | $\phantom{-}e^{4} - 2e^{3} - 18e^{2} + 19e + 76$ |
83 | $[83, 83, -2w - 13]$ | $\phantom{-}e^{4} - 2e^{3} - 18e^{2} + 19e + 76$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 6]$ | $-1$ |
$2$ | $[2, 2, w + 5]$ | $-1$ |