Base field 6.6.1868969.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 8x^{2} + x - 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[32, 32, -w^{4} + 5w^{2} - 4]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 12x^{5} + 22x^{4} - 204x^{3} - 891x^{2} - 1064x - 240\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}0$ |
13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $-\frac{2}{31}e^{5} - \frac{29}{62}e^{4} + \frac{21}{31}e^{3} + \frac{601}{62}e^{2} + \frac{467}{31}e - \frac{36}{31}$ |
23 | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}\frac{3}{124}e^{5} + \frac{45}{124}e^{4} + \frac{77}{124}e^{3} - \frac{939}{124}e^{2} - \frac{1381}{62}e - \frac{281}{31}$ |
31 | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ | $-\frac{3}{124}e^{5} - \frac{45}{124}e^{4} - \frac{77}{124}e^{3} + \frac{939}{124}e^{2} + \frac{1381}{62}e + \frac{157}{31}$ |
32 | $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ | $-\frac{3}{124}e^{5} - \frac{45}{124}e^{4} - \frac{77}{124}e^{3} + \frac{939}{124}e^{2} + \frac{1443}{62}e + \frac{281}{31}$ |
43 | $[43, 43, w^{4} - 5w^{2} + 3]$ | $-\frac{9}{124}e^{5} - \frac{73}{124}e^{4} + \frac{79}{124}e^{3} + \frac{1515}{124}e^{2} + \frac{537}{31}e - \frac{56}{31}$ |
47 | $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ | $\phantom{-}\frac{9}{124}e^{5} + \frac{73}{124}e^{4} - \frac{79}{124}e^{3} - \frac{1515}{124}e^{2} - \frac{599}{31}e - \frac{192}{31}$ |
49 | $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ | $-\frac{21}{124}e^{5} - \frac{191}{124}e^{4} + \frac{19}{124}e^{3} + \frac{3845}{124}e^{2} + \frac{2214}{31}e + \frac{882}{31}$ |
53 | $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ | $\phantom{-}\frac{13}{124}e^{5} + \frac{133}{124}e^{4} + \frac{3}{124}e^{3} - \frac{2891}{124}e^{2} - \frac{2781}{62}e - \frac{19}{31}$ |
59 | $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $-\frac{1}{124}e^{5} - \frac{15}{124}e^{4} - \frac{5}{124}e^{3} + \frac{313}{124}e^{2} + \frac{70}{31}e - \frac{51}{31}$ |
71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ | $\phantom{-}\frac{21}{124}e^{5} + \frac{191}{124}e^{4} - \frac{19}{124}e^{3} - \frac{3845}{124}e^{2} - \frac{2245}{31}e - \frac{882}{31}$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $-\frac{19}{124}e^{5} - \frac{161}{124}e^{4} + \frac{91}{124}e^{3} + \frac{3343}{124}e^{2} + \frac{3373}{62}e + \frac{395}{31}$ |
83 | $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ | $-\frac{3}{31}e^{5} - \frac{59}{62}e^{4} + \frac{1}{62}e^{3} + \frac{1227}{62}e^{2} + \frac{2455}{62}e + \frac{225}{31}$ |
83 | $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ | $\phantom{-}\frac{1}{31}e^{5} + \frac{15}{31}e^{4} + \frac{36}{31}e^{3} - \frac{282}{31}e^{2} - \frac{1117}{31}e - \frac{571}{31}$ |
89 | $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ | $-\frac{23}{124}e^{5} - \frac{221}{124}e^{4} + \frac{9}{124}e^{3} + \frac{4595}{124}e^{2} + \frac{2385}{31}e + \frac{656}{31}$ |
89 | $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ | $\phantom{-}\frac{21}{124}e^{5} + \frac{191}{124}e^{4} - \frac{19}{124}e^{3} - \frac{3845}{124}e^{2} - \frac{2245}{31}e - \frac{913}{31}$ |
89 | $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ | $\phantom{-}\frac{9}{124}e^{5} + \frac{73}{124}e^{4} - \frac{17}{124}e^{3} - \frac{1391}{124}e^{2} - \frac{1973}{62}e - \frac{657}{31}$ |
89 | $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ | $-\frac{2}{31}e^{5} - \frac{30}{31}e^{4} - \frac{41}{31}e^{3} + \frac{657}{31}e^{2} + \frac{1645}{31}e + \frac{336}{31}$ |
101 | $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ | $\phantom{-}\frac{15}{124}e^{5} + \frac{163}{124}e^{4} + \frac{75}{124}e^{3} - \frac{3393}{124}e^{2} - \frac{2042}{31}e - \frac{785}{31}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w]$ | $-1$ |