Base field 6.6.966125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} + 2x^{6} - 16x^{5} - 32x^{4} + 35x^{3} + 76x^{2} - 20x - 48\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{3} - 3w]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 9e^{4} + 8e^{3} + \frac{63}{2}e^{2} - \frac{25}{2}e - 24$ |
19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ | $\phantom{-}2$ |
25 | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $-\frac{3}{2}e^{6} + 26e^{4} - e^{3} - \frac{161}{2}e^{2} + 2e + 64$ |
29 | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $-\frac{3}{2}e^{6} + 26e^{4} - e^{3} - \frac{161}{2}e^{2} + 2e + 62$ |
31 | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $\phantom{-}\frac{9}{4}e^{6} + \frac{3}{2}e^{5} - 37e^{4} - 21e^{3} + \frac{371}{4}e^{2} + 24e - 64$ |
31 | $[31, 31, -w^{2} + 2]$ | $-\frac{5}{2}e^{6} - e^{5} + 41e^{4} + 13e^{3} - \frac{199}{2}e^{2} - 11e + 62$ |
59 | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $-1$ |
59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ | $\phantom{-}\frac{9}{4}e^{6} + \frac{5}{2}e^{5} - 36e^{4} - 36e^{3} + \frac{311}{4}e^{2} + 47e - 44$ |
59 | $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ | $-e^{6} - e^{5} + 16e^{4} + 14e^{3} - 35e^{2} - 13e + 20$ |
61 | $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ | $\phantom{-}\frac{3}{2}e^{6} - 26e^{4} + e^{3} + \frac{161}{2}e^{2} - 4e - 56$ |
64 | $[64, 2, 2]$ | $-\frac{7}{4}e^{6} - 2e^{5} + 28e^{4} + 29e^{3} - \frac{241}{4}e^{2} - \frac{77}{2}e + 33$ |
71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ | $-\frac{1}{2}e^{6} + 8e^{4} - \frac{35}{2}e^{2} - 5e + 8$ |
71 | $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ | $-\frac{5}{4}e^{6} - \frac{1}{2}e^{5} + 21e^{4} + 7e^{3} - \frac{231}{4}e^{2} - 10e + 44$ |
71 | $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ | $\phantom{-}\frac{7}{2}e^{6} + \frac{5}{2}e^{5} - 57e^{4} - 35e^{3} + \frac{271}{2}e^{2} + \frac{79}{2}e - 84$ |
71 | $[71, 71, w^{3} - 5w]$ | $-e^{4} + 16e^{2} + 2e - 28$ |
79 | $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}\frac{5}{2}e^{6} + \frac{3}{2}e^{5} - 41e^{4} - 21e^{3} + \frac{201}{2}e^{2} + \frac{49}{2}e - 68$ |
89 | $[89, 89, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}4e^{6} + e^{5} - 66e^{4} - 12e^{3} + 165e^{2} + 5e - 102$ |
101 | $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ | $\phantom{-}\frac{1}{2}e^{6} - 9e^{4} + \frac{65}{2}e^{2} + e - 34$ |
101 | $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ | $\phantom{-}\frac{7}{2}e^{6} + \frac{5}{2}e^{5} - 57e^{4} - 35e^{3} + \frac{269}{2}e^{2} + \frac{83}{2}e - 88$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$59$ | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $1$ |