Base field 6.6.485125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 8x^{3} + 2x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 27x^{5} + 8x^{4} + 144x^{3} - 80x^{2} - 192x + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{3}{8}e^{5} - \frac{25}{4}e^{4} - \frac{57}{8}e^{3} + \frac{53}{2}e^{2} + 15e - 24$ |
| 19 | $[19, 19, w^{3} - 3w - 1]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{3}{8}e^{5} - 6e^{4} - \frac{57}{8}e^{3} + \frac{83}{4}e^{2} + 15e - 12$ |
| 29 | $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $\phantom{-}\frac{11}{32}e^{6} + \frac{11}{16}e^{5} - \frac{265}{32}e^{4} - \frac{221}{16}e^{3} + 31e^{2} + \frac{63}{2}e - 28$ |
| 29 | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $\phantom{-}\frac{3}{16}e^{6} + \frac{3}{16}e^{5} - \frac{73}{16}e^{4} - \frac{49}{16}e^{3} + 17e^{2} + \frac{9}{2}e - 14$ |
| 31 | $[31, 31, -w^{4} + 4w^{2} + w - 3]$ | $\phantom{-}\frac{3}{32}e^{6} + \frac{1}{16}e^{5} - \frac{73}{32}e^{4} - \frac{15}{16}e^{3} + \frac{33}{4}e^{2} + \frac{3}{2}e - 6$ |
| 41 | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{3}{8}e^{5} - \frac{25}{4}e^{4} - \frac{57}{8}e^{3} + \frac{53}{2}e^{2} + 15e - 26$ |
| 49 | $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ | $-\frac{1}{16}e^{6} + \frac{27}{16}e^{4} - \frac{1}{2}e^{3} - 9e^{2} + 4e + 14$ |
| 59 | $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ | $-\frac{1}{4}e^{6} - \frac{5}{16}e^{5} + \frac{13}{2}e^{4} + \frac{95}{16}e^{3} - \frac{127}{4}e^{2} - \frac{31}{2}e + 34$ |
| 59 | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $-\frac{3}{16}e^{6} - \frac{3}{8}e^{5} + \frac{73}{16}e^{4} + \frac{61}{8}e^{3} - \frac{37}{2}e^{2} - 19e + 24$ |
| 59 | $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ | $-e^{2} + 8$ |
| 61 | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $-\frac{1}{4}e^{6} - \frac{5}{16}e^{5} + \frac{13}{2}e^{4} + \frac{95}{16}e^{3} - \frac{127}{4}e^{2} - \frac{27}{2}e + 36$ |
| 64 | $[64, 2, -2]$ | $-\frac{1}{2}e^{6} - \frac{3}{4}e^{5} + \frac{49}{4}e^{4} + \frac{57}{4}e^{3} - \frac{193}{4}e^{2} - 30e + 45$ |
| 71 | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $-1$ |
| 79 | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $-\frac{1}{8}e^{5} - \frac{1}{2}e^{4} + \frac{19}{8}e^{3} + \frac{21}{2}e^{2} - e - 20$ |
| 79 | $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ | $\phantom{-}\frac{11}{32}e^{6} + \frac{7}{16}e^{5} - \frac{273}{32}e^{4} - \frac{129}{16}e^{3} + \frac{135}{4}e^{2} + \frac{31}{2}e - 24$ |
| 79 | $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ | $-\frac{5}{16}e^{6} - \frac{1}{2}e^{5} + \frac{123}{16}e^{4} + 10e^{3} - \frac{123}{4}e^{2} - 25e + 34$ |
| 81 | $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ | $\phantom{-}\frac{3}{32}e^{6} + \frac{5}{16}e^{5} - \frac{65}{32}e^{4} - \frac{107}{16}e^{3} + \frac{7}{2}e^{2} + \frac{31}{2}e + 2$ |
| 89 | $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ | $\phantom{-}\frac{1}{8}e^{6} + \frac{7}{16}e^{5} - \frac{23}{8}e^{4} - \frac{149}{16}e^{3} + 10e^{2} + \frac{45}{2}e - 14$ |
| 101 | $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ | $-\frac{11}{16}e^{6} - \frac{7}{8}e^{5} + \frac{273}{16}e^{4} + \frac{129}{8}e^{3} - \frac{139}{2}e^{2} - 33e + 66$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $71$ | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $1$ |