Base field 6.6.722000.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 7x^{3} + 4x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, -3w^{5} + 2w^{4} + 18w^{3} - 15w^{2} - 14w + 7]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 4x^{6} - 12x^{5} + 46x^{4} + 35x^{3} - 98x^{2} - 16x + 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{5} + 6w^{3} - w^{2} - 6w]$ | $\phantom{-}e$ |
| 19 | $[19, 19, 3w^{5} - 2w^{4} - 19w^{3} + 14w^{2} + 18w - 9]$ | $-\frac{1}{8}e^{6} + \frac{3}{8}e^{5} + \frac{15}{8}e^{4} - \frac{31}{8}e^{3} - \frac{33}{4}e^{2} + 4e + 8$ |
| 29 | $[29, 29, -w^{2} - w + 2]$ | $-\frac{1}{8}e^{6} + \frac{3}{8}e^{5} + \frac{17}{8}e^{4} - \frac{35}{8}e^{3} - \frac{21}{2}e^{2} + \frac{13}{2}e + 8$ |
| 29 | $[29, 29, 2w^{5} - w^{4} - 13w^{3} + 7w^{2} + 14w - 3]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{8}e^{5} - \frac{25}{8}e^{4} + \frac{73}{8}e^{3} + \frac{79}{8}e^{2} - \frac{45}{4}e - 5$ |
| 29 | $[29, 29, -2w^{5} + w^{4} + 13w^{3} - 8w^{2} - 15w + 6]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{3}{8}e^{4} - \frac{7}{8}e^{3} + \frac{19}{8}e^{2} - \frac{9}{4}e - 1$ |
| 49 | $[49, 7, -3w^{5} + 2w^{4} + 19w^{3} - 15w^{2} - 19w + 9]$ | $-\frac{1}{8}e^{6} + \frac{3}{8}e^{5} + \frac{17}{8}e^{4} - \frac{39}{8}e^{3} - 10e^{2} + \frac{27}{2}e + 8$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 6w^{2} + 9w - 4]$ | $-\frac{1}{8}e^{6} + \frac{1}{2}e^{5} + e^{4} - \frac{19}{4}e^{3} + \frac{5}{8}e^{2} + \frac{27}{4}e - 1$ |
| 49 | $[49, 7, w^{2} - 3]$ | $-\frac{1}{4}e^{5} + \frac{1}{2}e^{4} + \frac{11}{4}e^{3} - 3e^{2} - 5e + 2$ |
| 59 | $[59, 59, -3w^{5} + 2w^{4} + 18w^{3} - 15w^{2} - 14w + 7]$ | $-1$ |
| 59 | $[59, 59, 2w^{5} - 12w^{3} + 3w^{2} + 12w - 3]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{1}{8}e^{4} - \frac{15}{8}e^{3} - \frac{3}{8}e^{2} + \frac{29}{4}e + 3$ |
| 59 | $[59, 59, -2w^{5} + w^{4} + 12w^{3} - 8w^{2} - 11w + 3]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{2}e^{5} - e^{4} + \frac{17}{4}e^{3} - \frac{1}{8}e^{2} - \frac{7}{4}e + 3$ |
| 61 | $[61, 61, -4w^{5} + 2w^{4} + 24w^{3} - 16w^{2} - 19w + 8]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{8}e^{5} - \frac{21}{8}e^{4} + \frac{5}{8}e^{3} + \frac{31}{2}e^{2} + \frac{9}{2}e - 12$ |
| 61 | $[61, 61, 5w^{5} - 3w^{4} - 31w^{3} + 22w^{2} + 27w - 13]$ | $-\frac{3}{8}e^{6} + \frac{11}{8}e^{5} + \frac{41}{8}e^{4} - \frac{123}{8}e^{3} - \frac{75}{4}e^{2} + 23e + 6$ |
| 61 | $[61, 61, 3w^{5} - w^{4} - 18w^{3} + 9w^{2} + 16w - 4]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{3}{4}e^{5} - e^{4} + 9e^{3} + \frac{3}{8}e^{2} - \frac{79}{4}e - 3$ |
| 71 | $[71, 71, 2w^{5} - 12w^{3} + 2w^{2} + 11w - 1]$ | $-\frac{1}{8}e^{6} + \frac{3}{4}e^{5} + \frac{3}{4}e^{4} - 8e^{3} + \frac{11}{8}e^{2} + \frac{49}{4}e - 1$ |
| 71 | $[71, 71, 3w^{5} - 2w^{4} - 18w^{3} + 15w^{2} + 13w - 9]$ | $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{17}{4}e^{2} + \frac{11}{2}e - 6$ |
| 71 | $[71, 71, -w^{5} + w^{4} + 6w^{3} - 7w^{2} - 6w + 5]$ | $\phantom{-}\frac{3}{8}e^{6} - \frac{11}{8}e^{5} - \frac{37}{8}e^{4} + \frac{115}{8}e^{3} + \frac{57}{4}e^{2} - 20e - 8$ |
| 79 | $[79, 79, -w^{5} + 7w^{3} - w^{2} - 10w]$ | $-e^{3} + e^{2} + 8e$ |
| 79 | $[79, 79, 4w^{5} - 2w^{4} - 25w^{3} + 15w^{2} + 23w - 9]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{3}{4}e^{5} - \frac{15}{4}e^{4} + \frac{31}{4}e^{3} + \frac{33}{2}e^{2} - 10e - 8$ |
| 79 | $[79, 79, -w^{5} + 6w^{3} - 2w^{2} - 7w + 4]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{5}{8}e^{5} - \frac{9}{8}e^{4} + \frac{57}{8}e^{3} + e^{2} - \frac{33}{2}e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, -3w^{5} + 2w^{4} + 18w^{3} - 15w^{2} - 14w + 7]$ | $1$ |