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:
| \(x^{6} + 6x^{5} - 57x^{4} - 466x^{3} - 282x^{2} + 3822x + 6697\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -\frac{6}{19}w^{5} + \frac{4}{19}w^{4} + \frac{45}{19}w^{3} - \frac{6}{19}w^{2} - \frac{12}{19}w + \frac{28}{19}]$ | $\phantom{-}0$ |
| 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 | $[19, 19, -\frac{10}{19}w^{5} - \frac{6}{19}w^{4} + \frac{94}{19}w^{3} + \frac{85}{19}w^{2} - \frac{77}{19}w - \frac{42}{19}]$ | $-\frac{88}{1917}e^{5} + \frac{70}{1917}e^{4} + \frac{4976}{1917}e^{3} + \frac{6032}{1917}e^{2} - \frac{39701}{1917}e - \frac{63892}{1917}$ |
| 19 | $[19, 19, -\frac{16}{19}w^{5} - \frac{2}{19}w^{4} + \frac{139}{19}w^{3} + \frac{79}{19}w^{2} - \frac{108}{19}w - \frac{33}{19}]$ | $-\frac{4}{213}e^{5} - \frac{55}{639}e^{4} + \frac{827}{639}e^{3} + \frac{455}{71}e^{2} - \frac{5701}{639}e - \frac{31084}{639}$ |
| 19 | $[19, 19, -\frac{4}{19}w^{5} + \frac{9}{19}w^{4} + \frac{30}{19}w^{3} - \frac{61}{19}w^{2} - \frac{8}{19}w + \frac{44}{19}]$ | $-\frac{50}{639}e^{5} - \frac{11}{71}e^{4} + \frac{3221}{639}e^{3} + \frac{10495}{639}e^{2} - \frac{8774}{213}e - \frac{89023}{639}$ |
| 19 | $[19, 19, -\frac{8}{19}w^{5} - \frac{1}{19}w^{4} + \frac{79}{19}w^{3} + \frac{30}{19}w^{2} - \frac{111}{19}w - \frac{7}{19}]$ | $\phantom{-}\frac{152}{1917}e^{5} + \frac{247}{1917}e^{4} - \frac{9505}{1917}e^{3} - \frac{29647}{1917}e^{2} + \frac{73183}{1917}e + \frac{249506}{1917}$ |
| 19 | $[19, 19, \frac{2}{19}w^{5} + \frac{5}{19}w^{4} - \frac{15}{19}w^{3} - \frac{55}{19}w^{2} - \frac{34}{19}w + \frac{35}{19}]$ | $\phantom{-}\frac{122}{1917}e^{5} + \frac{145}{1917}e^{4} - \frac{7615}{1917}e^{3} - \frac{20155}{1917}e^{2} + \frac{60670}{1917}e + \frac{163205}{1917}$ |
| 64 | $[64, 2, 2]$ | $\phantom{-}1$ |
| 71 | $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$ | $-\frac{296}{1917}e^{5} - \frac{481}{1917}e^{4} + \frac{18790}{1917}e^{3} + \frac{57061}{1917}e^{2} - \frac{156505}{1917}e - \frac{494075}{1917}$ |
| 71 | $[71, 71, -\frac{11}{19}w^{5} + \frac{20}{19}w^{4} + \frac{92}{19}w^{3} - \frac{125}{19}w^{2} - \frac{117}{19}w + \frac{64}{19}]$ | $\phantom{-}\frac{212}{1917}e^{5} + \frac{25}{1917}e^{4} - \frac{12646}{1917}e^{3} - \frac{23071}{1917}e^{2} + \frac{101617}{1917}e + \frac{193985}{1917}$ |
| 71 | $[71, 71, \frac{12}{19}w^{5} - \frac{8}{19}w^{4} - \frac{109}{19}w^{3} + \frac{12}{19}w^{2} + \frac{138}{19}w + \frac{1}{19}]$ | $\phantom{-}\frac{164}{1917}e^{5} + \frac{160}{1917}e^{4} - \frac{9835}{1917}e^{3} - \frac{27565}{1917}e^{2} + \frac{73204}{1917}e + \frac{249563}{1917}$ |
| 71 | $[71, 71, \frac{22}{19}w^{5} - \frac{21}{19}w^{4} - \frac{184}{19}w^{3} + \frac{79}{19}w^{2} + \frac{177}{19}w - \frac{52}{19}]$ | $-\frac{376}{1917}e^{5} - \frac{185}{1917}e^{4} + \frac{22481}{1917}e^{3} + \frac{50636}{1917}e^{2} - \frac{174821}{1917}e - \frac{443548}{1917}$ |
| 71 | $[71, 71, w^{5} - w^{4} - 8w^{3} + 4w^{2} + 6w - 3]$ | $\phantom{-}\frac{112}{1917}e^{5} + \frac{395}{1917}e^{4} - \frac{7553}{1917}e^{3} - \frac{32540}{1917}e^{2} + \frac{61469}{1917}e + \frac{263374}{1917}$ |
| 71 | $[71, 71, -\frac{24}{19}w^{5} + \frac{16}{19}w^{4} + \frac{199}{19}w^{3} - \frac{24}{19}w^{2} - \frac{162}{19}w - \frac{21}{19}]$ | $\phantom{-}\frac{184}{1917}e^{5} + \frac{86}{1917}e^{4} - \frac{11237}{1917}e^{3} - \frac{24521}{1917}e^{2} + \frac{95036}{1917}e + \frac{230701}{1917}$ |
| 89 | $[89, 89, \frac{13}{19}w^{5} + \frac{4}{19}w^{4} - \frac{126}{19}w^{3} - \frac{82}{19}w^{2} + \frac{159}{19}w + \frac{66}{19}]$ | $-\frac{203}{1917}e^{5} - \frac{463}{1917}e^{4} + \frac{13144}{1917}e^{3} + \frac{45400}{1917}e^{2} - \frac{104530}{1917}e - \frac{367484}{1917}$ |
| 89 | $[89, 89, -\frac{17}{19}w^{5} + \frac{5}{19}w^{4} + \frac{137}{19}w^{3} + \frac{40}{19}w^{2} - \frac{53}{19}w - \frac{41}{19}]$ | $-\frac{101}{1917}e^{5} - \frac{244}{1917}e^{4} + \frac{6718}{1917}e^{3} + \frac{23479}{1917}e^{2} - \frac{56746}{1917}e - \frac{200966}{1917}$ |
| 89 | $[89, 89, -\frac{29}{19}w^{5} + \frac{13}{19}w^{4} + \frac{246}{19}w^{3} + \frac{9}{19}w^{2} - \frac{210}{19}w + \frac{15}{19}]$ | $\phantom{-}\frac{407}{1917}e^{5} + \frac{475}{1917}e^{4} - \frac{25144}{1917}e^{3} - \frac{68794}{1917}e^{2} + \frac{198394}{1917}e + \frac{587630}{1917}$ |
| 89 | $[89, 89, \frac{3}{19}w^{5} + \frac{17}{19}w^{4} - \frac{32}{19}w^{3} - \frac{149}{19}w^{2} - \frac{13}{19}w + \frac{62}{19}]$ | $\phantom{-}\frac{25}{1917}e^{5} + \frac{14}{1917}e^{4} - \frac{1646}{1917}e^{3} - \frac{3224}{1917}e^{2} + \frac{20048}{1917}e + \frac{36595}{1917}$ |
| 89 | $[89, 89, \frac{7}{19}w^{5} - \frac{11}{19}w^{4} - \frac{62}{19}w^{3} + \frac{64}{19}w^{2} + \frac{71}{19}w - \frac{39}{19}]$ | $-\frac{43}{1917}e^{5} + \frac{10}{1917}e^{4} + \frac{2354}{1917}e^{3} + \frac{5213}{1917}e^{2} - \frac{17630}{1917}e - \frac{59152}{1917}$ |
| 89 | $[89, 89, -\frac{9}{19}w^{5} + \frac{6}{19}w^{4} + \frac{77}{19}w^{3} - \frac{28}{19}w^{2} - \frac{56}{19}w + \frac{42}{19}]$ | $-\frac{85}{1917}e^{5} + \frac{208}{1917}e^{4} + \frac{4574}{1917}e^{3} - \frac{2074}{1917}e^{2} - \frac{39536}{1917}e + \frac{3377}{1917}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $64$ | $[64, 2, 2]$ | $-1$ |