Base field 6.6.820125.1
Generator \(w\), with minimal polynomial \(x^{6} - 9x^{4} - 4x^{3} + 9x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[64, 2, 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 3x^{5} - 58x^{4} + 290x^{3} - 86x^{2} - 872x + 103\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -\frac{6}{19}w^{5} + \frac{4}{19}w^{4} + \frac{45}{19}w^{3} - \frac{6}{19}w^{2} - \frac{12}{19}w + \frac{28}{19}]$ | $-3$ |
19 | $[19, 19, -\frac{20}{19}w^{5} + \frac{7}{19}w^{4} + \frac{169}{19}w^{3} + \frac{18}{19}w^{2} - \frac{116}{19}w + \frac{11}{19}]$ | $\phantom{-}e$ |
19 | $[19, 19, -\frac{10}{19}w^{5} - \frac{6}{19}w^{4} + \frac{94}{19}w^{3} + \frac{85}{19}w^{2} - \frac{77}{19}w - \frac{42}{19}]$ | $-\frac{1}{31}e^{5} - \frac{4}{155}e^{4} + \frac{54}{31}e^{3} - \frac{89}{31}e^{2} - \frac{227}{31}e + \frac{729}{155}$ |
19 | $[19, 19, -\frac{16}{19}w^{5} - \frac{2}{19}w^{4} + \frac{139}{19}w^{3} + \frac{79}{19}w^{2} - \frac{108}{19}w - \frac{33}{19}]$ | $\phantom{-}\frac{13}{155}e^{5} + \frac{14}{155}e^{4} - \frac{145}{31}e^{3} + \frac{166}{31}e^{2} + \frac{3757}{155}e + \frac{106}{155}$ |
19 | $[19, 19, -\frac{4}{19}w^{5} + \frac{9}{19}w^{4} + \frac{30}{19}w^{3} - \frac{61}{19}w^{2} - \frac{8}{19}w + \frac{44}{19}]$ | $\phantom{-}\frac{18}{155}e^{5} + \frac{17}{155}e^{4} - \frac{196}{31}e^{3} + \frac{268}{31}e^{2} + \frac{3962}{155}e + \frac{328}{155}$ |
19 | $[19, 19, -\frac{8}{19}w^{5} - \frac{1}{19}w^{4} + \frac{79}{19}w^{3} + \frac{30}{19}w^{2} - \frac{111}{19}w - \frac{7}{19}]$ | $-\frac{24}{155}e^{5} - \frac{18}{155}e^{4} + \frac{268}{31}e^{3} - \frac{387}{31}e^{2} - \frac{6006}{155}e + \frac{498}{155}$ |
19 | $[19, 19, \frac{2}{19}w^{5} + \frac{5}{19}w^{4} - \frac{15}{19}w^{3} - \frac{55}{19}w^{2} - \frac{34}{19}w + \frac{35}{19}]$ | $-\frac{2}{155}e^{5} - \frac{9}{155}e^{4} + \frac{19}{31}e^{3} + \frac{42}{31}e^{2} - \frac{733}{155}e - \frac{1196}{155}$ |
64 | $[64, 2, 2]$ | $-1$ |
71 | $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$ | $-\frac{22}{155}e^{5} - \frac{26}{155}e^{4} + \frac{238}{31}e^{3} - \frac{270}{31}e^{2} - \frac{5118}{155}e - \frac{1824}{155}$ |
71 | $[71, 71, -\frac{11}{19}w^{5} + \frac{20}{19}w^{4} + \frac{92}{19}w^{3} - \frac{125}{19}w^{2} - \frac{117}{19}w + \frac{64}{19}]$ | $\phantom{-}\frac{18}{155}e^{5} + \frac{26}{155}e^{4} - \frac{192}{31}e^{3} + \frac{182}{31}e^{2} + \frac{4272}{155}e + \frac{1224}{155}$ |
71 | $[71, 71, \frac{12}{19}w^{5} - \frac{8}{19}w^{4} - \frac{109}{19}w^{3} + \frac{12}{19}w^{2} + \frac{138}{19}w + \frac{1}{19}]$ | $\phantom{-}\frac{6}{31}e^{5} + \frac{28}{155}e^{4} - \frac{336}{31}e^{3} + \frac{420}{31}e^{2} + \frac{1672}{31}e - \frac{118}{155}$ |
71 | $[71, 71, \frac{22}{19}w^{5} - \frac{21}{19}w^{4} - \frac{184}{19}w^{3} + \frac{79}{19}w^{2} + \frac{177}{19}w - \frac{52}{19}]$ | $\phantom{-}\frac{14}{155}e^{5} + \frac{8}{155}e^{4} - \frac{154}{31}e^{3} + \frac{266}{31}e^{2} + \frac{3116}{155}e - \frac{1478}{155}$ |
71 | $[71, 71, w^{5} - w^{4} - 8w^{3} + 4w^{2} + 6w - 3]$ | $\phantom{-}\frac{4}{155}e^{5} - \frac{46}{31}e^{3} + \frac{88}{31}e^{2} + \frac{536}{155}e - \frac{4}{31}$ |
71 | $[71, 71, -\frac{24}{19}w^{5} + \frac{16}{19}w^{4} + \frac{199}{19}w^{3} - \frac{24}{19}w^{2} - \frac{162}{19}w - \frac{21}{19}]$ | $-\frac{44}{155}e^{5} - \frac{36}{155}e^{4} + \frac{490}{31}e^{3} - \frac{686}{31}e^{2} - \frac{11166}{155}e + \frac{666}{155}$ |
89 | $[89, 89, \frac{13}{19}w^{5} + \frac{4}{19}w^{4} - \frac{126}{19}w^{3} - \frac{82}{19}w^{2} + \frac{159}{19}w + \frac{66}{19}]$ | $\phantom{-}\frac{3}{31}e^{5} + \frac{4}{155}e^{4} - \frac{169}{31}e^{3} + \frac{309}{31}e^{2} + \frac{557}{31}e + \frac{306}{155}$ |
89 | $[89, 89, -\frac{17}{19}w^{5} + \frac{5}{19}w^{4} + \frac{137}{19}w^{3} + \frac{40}{19}w^{2} - \frac{53}{19}w - \frac{41}{19}]$ | $-\frac{12}{31}e^{5} - \frac{44}{155}e^{4} + \frac{667}{31}e^{3} - \frac{996}{31}e^{2} - \frac{2879}{31}e + \frac{2464}{155}$ |
89 | $[89, 89, -\frac{29}{19}w^{5} + \frac{13}{19}w^{4} + \frac{246}{19}w^{3} + \frac{9}{19}w^{2} - \frac{210}{19}w + \frac{15}{19}]$ | $\phantom{-}\frac{5}{31}e^{5} + \frac{12}{155}e^{4} - \frac{277}{31}e^{3} + \frac{487}{31}e^{2} + \frac{1073}{31}e - \frac{1152}{155}$ |
89 | $[89, 89, \frac{3}{19}w^{5} + \frac{17}{19}w^{4} - \frac{32}{19}w^{3} - \frac{149}{19}w^{2} - \frac{13}{19}w + \frac{62}{19}]$ | $-\frac{17}{155}e^{5} - \frac{22}{155}e^{4} + \frac{184}{31}e^{3} - \frac{181}{31}e^{2} - \frac{4138}{155}e - \frac{1623}{155}$ |
89 | $[89, 89, \frac{7}{19}w^{5} - \frac{11}{19}w^{4} - \frac{62}{19}w^{3} + \frac{64}{19}w^{2} + \frac{71}{19}w - \frac{39}{19}]$ | $\phantom{-}\frac{14}{155}e^{5} + \frac{4}{31}e^{4} - \frac{159}{31}e^{3} + \frac{110}{31}e^{2} + \frac{5131}{155}e + \frac{336}{31}$ |
89 | $[89, 89, -\frac{9}{19}w^{5} + \frac{6}{19}w^{4} + \frac{77}{19}w^{3} - \frac{28}{19}w^{2} - \frac{56}{19}w + \frac{42}{19}]$ | $\phantom{-}\frac{23}{155}e^{5} + \frac{6}{31}e^{4} - \frac{246}{31}e^{3} + \frac{271}{31}e^{2} + \frac{5252}{155}e + \frac{285}{31}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$64$ | $[64, 2, 2]$ | $1$ |