Base field 6.6.592661.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 2x^{6} - 28x^{5} - 59x^{4} + 176x^{3} + 476x^{2} + 144x - 176\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{5} - 5w^{3} + 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{3} + 3w]$ | $\phantom{-}\frac{39}{1336}e^{6} + \frac{3}{167}e^{5} - \frac{307}{334}e^{4} - \frac{909}{1336}e^{3} + \frac{5089}{668}e^{2} + \frac{1137}{167}e - \frac{1399}{167}$ |
| 25 | $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $\phantom{-}\frac{71}{334}e^{6} + \frac{9}{167}e^{5} - \frac{1045}{167}e^{4} - \frac{807}{334}e^{3} + \frac{7449}{167}e^{2} + \frac{5916}{167}e - \frac{4364}{167}$ |
| 31 | $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ | $-\frac{73}{334}e^{6} - \frac{77}{668}e^{5} + \frac{2123}{334}e^{4} + \frac{1239}{334}e^{3} - \frac{29885}{668}e^{2} - \frac{6753}{167}e + \frac{4287}{167}$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-\frac{149}{668}e^{6} - \frac{33}{334}e^{5} + \frac{1053}{167}e^{4} + \frac{2291}{668}e^{3} - \frac{7060}{167}e^{2} - \frac{6838}{167}e + \frac{3436}{167}$ |
| 37 | $[37, 37, w^{4} - 5w^{2} + w + 3]$ | $-\frac{65}{668}e^{6} - \frac{10}{167}e^{5} + \frac{456}{167}e^{4} + \frac{847}{668}e^{3} - \frac{6255}{334}e^{2} - \frac{1786}{167}e + \frac{2548}{167}$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ | $-1$ |
| 47 | $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ | $\phantom{-}\frac{11}{334}e^{6} - \frac{25}{668}e^{5} - \frac{265}{334}e^{4} + \frac{463}{334}e^{3} + \frac{2911}{668}e^{2} - \frac{1492}{167}e - \frac{1664}{167}$ |
| 49 | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ | $\phantom{-}\frac{29}{334}e^{6} + \frac{5}{334}e^{5} - \frac{448}{167}e^{4} - \frac{419}{334}e^{3} + \frac{6699}{334}e^{2} + \frac{3202}{167}e - \frac{1806}{167}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ | $-\frac{577}{1336}e^{6} - \frac{139}{668}e^{5} + \frac{4071}{334}e^{4} + \frac{7899}{1336}e^{3} - \frac{27769}{334}e^{2} - \frac{21247}{334}e + \frac{9539}{167}$ |
| 59 | $[59, 59, w^{4} - 5w^{2} - w + 5]$ | $\phantom{-}\frac{237}{668}e^{6} + \frac{133}{668}e^{5} - \frac{3333}{334}e^{4} - \frac{3931}{668}e^{3} + \frac{44059}{668}e^{2} + \frac{10389}{167}e - \frac{4748}{167}$ |
| 61 | $[61, 61, w^{3} - w^{2} - 3w]$ | $\phantom{-}\frac{233}{668}e^{6} + \frac{23}{167}e^{5} - \frac{1650}{167}e^{4} - \frac{3067}{668}e^{3} + \frac{22319}{334}e^{2} + \frac{9719}{167}e - \frac{5994}{167}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{17}{668}e^{6} + \frac{49}{668}e^{5} - \frac{91}{167}e^{4} - \frac{499}{668}e^{3} + \frac{1923}{668}e^{2} - \frac{1653}{334}e - \frac{1134}{167}$ |
| 67 | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ | $\phantom{-}\frac{305}{668}e^{6} + \frac{81}{334}e^{5} - \frac{2114}{167}e^{4} - \frac{4591}{668}e^{3} + \frac{13731}{167}e^{2} + \frac{12427}{167}e - \frac{5610}{167}$ |
| 67 | $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ | $-\frac{203}{1336}e^{6} - \frac{101}{668}e^{5} + \frac{1401}{334}e^{4} + \frac{4937}{1336}e^{3} - \frac{9427}{334}e^{2} - \frac{9871}{334}e + \frac{3077}{167}$ |
| 73 | $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ | $\phantom{-}\frac{97}{334}e^{6} + \frac{17}{167}e^{5} - \frac{1343}{167}e^{4} - \frac{1079}{334}e^{3} + \frac{8782}{167}e^{2} + \frac{7111}{167}e - \frac{4532}{167}$ |
| 73 | $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ | $\phantom{-}\frac{27}{668}e^{6} + \frac{17}{167}e^{5} - \frac{174}{167}e^{4} - \frac{1657}{668}e^{3} + \frac{2033}{334}e^{2} + \frac{2435}{167}e + \frac{1480}{167}$ |
| 83 | $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ | $-\frac{209}{1336}e^{6} + \frac{77}{668}e^{5} + \frac{1551}{334}e^{4} - \frac{2117}{1336}e^{3} - \frac{10859}{334}e^{2} - \frac{5031}{334}e + \frac{3395}{167}$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ | $\phantom{-}\frac{17}{1336}e^{6} + \frac{27}{167}e^{5} - \frac{91}{334}e^{4} - \frac{4507}{1336}e^{3} + \frac{2047}{668}e^{2} + \frac{1883}{167}e - \frac{1903}{167}$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ | $\phantom{-}\frac{143}{668}e^{6} + \frac{22}{167}e^{5} - \frac{1070}{167}e^{4} - \frac{3333}{668}e^{3} + \frac{15765}{334}e^{2} + \frac{9006}{167}e - \frac{4136}{167}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $43$ | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ | $1$ |