Base field \(\Q(\sqrt{123}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 123\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[6, 6, w + 3]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 4x^{7} - 16x^{6} + 110x^{5} - 202x^{4} + 126x^{3} + 14x^{2} - 36x + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 11]$ | $-1$ |
3 | $[3, 3, w]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 5]$ | $\phantom{-}e^{7} - 3e^{6} - 19e^{5} + 91e^{4} - 111e^{3} + 15e^{2} + 29e - 6$ |
17 | $[17, 17, w + 2]$ | $-\frac{5}{6}e^{7} + \frac{5}{2}e^{6} + \frac{47}{3}e^{5} - \frac{227}{3}e^{4} + \frac{289}{3}e^{3} - \frac{61}{3}e^{2} - 28e + \frac{25}{3}$ |
17 | $[17, 17, w + 15]$ | $\phantom{-}\frac{5}{6}e^{7} - \frac{5}{2}e^{6} - \frac{47}{3}e^{5} + \frac{227}{3}e^{4} - \frac{289}{3}e^{3} + \frac{61}{3}e^{2} + 28e - \frac{43}{3}$ |
19 | $[19, 19, w + 3]$ | $-\frac{1}{2}e^{6} + e^{5} + 10e^{4} - 35e^{3} + 31e^{2} - e - 7$ |
19 | $[19, 19, w + 16]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - 10e^{4} + 35e^{3} - 31e^{2} + e + 7$ |
23 | $[23, 23, -w - 10]$ | $-\frac{7}{6}e^{7} + \frac{11}{3}e^{6} + 22e^{5} - 110e^{4} + \frac{412}{3}e^{3} - \frac{41}{3}e^{2} - \frac{121}{3}e + \frac{16}{3}$ |
23 | $[23, 23, w - 10]$ | $-\frac{5}{6}e^{7} + \frac{10}{3}e^{6} + 14e^{5} - 93e^{4} + \frac{464}{3}e^{3} - \frac{175}{3}e^{2} - \frac{143}{3}e + \frac{62}{3}$ |
25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{3}{2}e^{6} - 9e^{5} + 45e^{4} - 66e^{3} + 32e^{2} + 8e - 7$ |
29 | $[29, 29, w + 6]$ | $-\frac{1}{6}e^{7} + \frac{1}{3}e^{6} + \frac{11}{3}e^{5} - \frac{35}{3}e^{4} + 4e^{3} + \frac{31}{3}e^{2} - \frac{20}{3}e + 2$ |
29 | $[29, 29, w + 23]$ | $\phantom{-}\frac{25}{6}e^{7} - \frac{40}{3}e^{6} - \frac{230}{3}e^{5} + \frac{1187}{3}e^{4} - 539e^{3} + \frac{422}{3}e^{2} + \frac{422}{3}e - 54$ |
37 | $[37, 37, 9w + 100]$ | $-\frac{5}{2}e^{7} + 9e^{6} + 44e^{5} - 258e^{4} + 394e^{3} - 133e^{2} - 111e + 50$ |
37 | $[37, 37, -2w - 23]$ | $\phantom{-}\frac{1}{2}e^{7} - 2e^{6} - 8e^{5} + 55e^{4} - 102e^{3} + 61e^{2} + 23e - 20$ |
41 | $[41, 41, w]$ | $-e^{7} + 4e^{6} + 16e^{5} - 111e^{4} + 202e^{3} - 106e^{2} - 44e + 34$ |
53 | $[53, 53, w + 21]$ | $-\frac{13}{6}e^{7} + 7e^{6} + \frac{118}{3}e^{5} - \frac{619}{3}e^{4} + \frac{881}{3}e^{3} - \frac{311}{3}e^{2} - 64e + \frac{110}{3}$ |
53 | $[53, 53, w + 32]$ | $\phantom{-}\frac{1}{6}e^{7} - e^{6} - \frac{7}{3}e^{5} + \frac{76}{3}e^{4} - \frac{152}{3}e^{3} + \frac{74}{3}e^{2} + 18e - \frac{50}{3}$ |
59 | $[59, 59, -w - 8]$ | $-\frac{11}{3}e^{7} + \frac{65}{6}e^{6} + \frac{209}{3}e^{5} - \frac{989}{3}e^{4} + 403e^{3} - \frac{197}{3}e^{2} - \frac{305}{3}e + 23$ |
59 | $[59, 59, w - 8]$ | $\phantom{-}\frac{5}{3}e^{7} - \frac{41}{6}e^{6} - \frac{83}{3}e^{5} + \frac{569}{3}e^{4} - 321e^{3} + \frac{359}{3}e^{2} + \frac{293}{3}e - 39$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 11]$ | $1$ |
$3$ | $[3, 3, w]$ | $-1$ |