Base field \(\Q(\sqrt{82}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 82\); narrow class number \(4\) and class number \(4\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 2x^{3} + 2x^{2} - 12x + 36\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{3}e^{2} + \frac{1}{3}e - 2$ |
11 | $[11, 11, w + 4]$ | $\phantom{-}\frac{1}{42}e^{3} + \frac{4}{21}e^{2} - \frac{17}{21}e + \frac{6}{7}$ |
11 | $[11, 11, w + 7]$ | $-\frac{4}{21}e^{3} - \frac{11}{21}e^{2} - \frac{11}{21}e + \frac{22}{7}$ |
13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{1}{42}e^{3} + \frac{4}{21}e^{2} + \frac{4}{21}e - \frac{8}{7}$ |
13 | $[13, 13, w + 11]$ | $-\frac{1}{42}e^{3} - \frac{4}{21}e^{2} - \frac{4}{21}e - \frac{6}{7}$ |
19 | $[19, 19, w + 5]$ | $\phantom{-}\frac{1}{14}e^{3} + \frac{4}{7}e^{2} - \frac{3}{7}e + \frac{18}{7}$ |
19 | $[19, 19, w + 14]$ | $-\frac{5}{21}e^{3} - \frac{19}{21}e^{2} - \frac{19}{21}e + \frac{38}{7}$ |
23 | $[23, 23, w + 6]$ | $\phantom{-}\frac{1}{21}e^{3} - \frac{13}{21}e^{2} + \frac{8}{21}e - \frac{2}{7}$ |
23 | $[23, 23, w + 17]$ | $\phantom{-}\frac{2}{7}e^{3} + \frac{9}{7}e^{2} + \frac{16}{7}e - \frac{12}{7}$ |
25 | $[25, 5, -5]$ | $-4$ |
29 | $[29, 29, w + 13]$ | $-\frac{5}{21}e^{3} + \frac{2}{21}e^{2} + \frac{2}{21}e - \frac{4}{7}$ |
29 | $[29, 29, w + 16]$ | $-\frac{2}{21}e^{3} - \frac{16}{21}e^{2} - \frac{58}{21}e - \frac{24}{7}$ |
31 | $[31, 31, w + 12]$ | $\phantom{-}\frac{1}{7}e^{3} + \frac{1}{7}e^{2} + \frac{8}{7}e - \frac{6}{7}$ |
31 | $[31, 31, w + 19]$ | $\phantom{-}\frac{4}{21}e^{3} + \frac{11}{21}e^{2} + \frac{32}{21}e - \frac{8}{7}$ |
41 | $[41, 41, w]$ | $-\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{8}{3}e + 2$ |
49 | $[49, 7, -7]$ | $-4$ |
53 | $[53, 53, w + 20]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{2}{3}e - 4$ |
53 | $[53, 53, w + 33]$ | $\phantom{-}2e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $1$ |