Base field \(\Q(\sqrt{109}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[21, 21, w + 2]$ |
Dimension: | $3$ |
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:
\(x^{3} - 9x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 5]$ | $\phantom{-}1$ |
4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - \frac{5}{3}$ |
5 | $[5, 5, -3w + 17]$ | $-3$ |
5 | $[5, 5, -3w - 14]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{1}{3}e - \frac{10}{3}$ |
7 | $[7, 7, w - 5]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 4]$ | $-\frac{1}{3}e^{2} + \frac{2}{3}e + \frac{5}{3}$ |
29 | $[29, 29, -w - 7]$ | $-\frac{4}{3}e^{2} + \frac{5}{3}e + \frac{26}{3}$ |
29 | $[29, 29, -w + 8]$ | $\phantom{-}e^{2} - e - 9$ |
31 | $[31, 31, -5w + 28]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e - \frac{8}{3}$ |
31 | $[31, 31, -5w - 23]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{4}{3}e - \frac{17}{3}$ |
43 | $[43, 43, 6w + 29]$ | $\phantom{-}e - 5$ |
43 | $[43, 43, -6w + 35]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e - \frac{26}{3}$ |
61 | $[61, 61, 3w - 19]$ | $-\frac{2}{3}e^{2} - \frac{2}{3}e + \frac{10}{3}$ |
61 | $[61, 61, -3w - 16]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{2}{3}e + \frac{11}{3}$ |
71 | $[71, 71, -7w - 34]$ | $\phantom{-}\frac{4}{3}e^{2} + \frac{7}{3}e - \frac{11}{3}$ |
71 | $[71, 71, 7w - 41]$ | $\phantom{-}e - 4$ |
73 | $[73, 73, 2w - 7]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{16}{3}e - \frac{16}{3}$ |
73 | $[73, 73, -2w - 5]$ | $\phantom{-}\frac{5}{3}e^{2} - \frac{1}{3}e - \frac{16}{3}$ |
83 | $[83, 83, -w - 10]$ | $\phantom{-}2e^{2} - e - 16$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 5]$ | $-1$ |
$7$ | $[7, 7, w - 5]$ | $-1$ |