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: | $[31, 31, -w^{2} + 2]$ |
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:
\(x^{7} + 6x^{6} - x^{5} - 43x^{4} - 16x^{3} + 53x^{2} + 25x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{3} - 3w]$ | $-e - 2$ |
19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ | $\phantom{-}\frac{1}{3}e^{6} + 2e^{5} - \frac{40}{3}e^{3} - \frac{19}{3}e^{2} + \frac{49}{3}e + 2$ |
25 | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $-\frac{1}{3}e^{6} - \frac{7}{3}e^{5} - e^{4} + \frac{46}{3}e^{3} + \frac{32}{3}e^{2} - 15e - \frac{28}{3}$ |
29 | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $-e^{6} - \frac{16}{3}e^{5} + 4e^{4} + 40e^{3} - \frac{8}{3}e^{2} - \frac{152}{3}e - \frac{22}{3}$ |
31 | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $\phantom{-}\frac{1}{3}e^{6} + \frac{5}{3}e^{5} - e^{4} - \frac{37}{3}e^{3} - 6e^{2} + \frac{62}{3}e + \frac{20}{3}$ |
31 | $[31, 31, -w^{2} + 2]$ | $\phantom{-}1$ |
59 | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $-\frac{2}{3}e^{6} - \frac{10}{3}e^{5} + 2e^{4} + \frac{62}{3}e^{3} + 3e^{2} - \frac{46}{3}e - \frac{28}{3}$ |
59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ | $-\frac{1}{3}e^{6} - 2e^{5} + \frac{40}{3}e^{3} + \frac{22}{3}e^{2} - \frac{46}{3}e - 8$ |
59 | $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ | $\phantom{-}e^{6} + 6e^{5} - 2e^{4} - 45e^{3} - 8e^{2} + 53e + 18$ |
61 | $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ | $-\frac{1}{3}e^{6} - \frac{5}{3}e^{5} + e^{4} + \frac{34}{3}e^{3} + 3e^{2} - \frac{50}{3}e - \frac{26}{3}$ |
64 | $[64, 2, 2]$ | $-\frac{1}{3}e^{6} - 2e^{5} + e^{4} + \frac{46}{3}e^{3} - \frac{8}{3}e^{2} - \frac{64}{3}e + 1$ |
71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ | $\phantom{-}2e^{6} + \frac{35}{3}e^{5} - 5e^{4} - 87e^{3} - \frac{26}{3}e^{2} + \frac{322}{3}e + \frac{68}{3}$ |
71 | $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ | $-\frac{1}{3}e^{6} - 2e^{5} + \frac{43}{3}e^{3} + \frac{25}{3}e^{2} - \frac{70}{3}e - 8$ |
71 | $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ | $-\frac{2}{3}e^{5} - 2e^{4} + 6e^{3} + \frac{35}{3}e^{2} - \frac{43}{3}e - \frac{38}{3}$ |
71 | $[71, 71, w^{3} - 5w]$ | $-e^{6} - \frac{17}{3}e^{5} + 2e^{4} + 41e^{3} + \frac{38}{3}e^{2} - \frac{160}{3}e - \frac{56}{3}$ |
79 | $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}\frac{2}{3}e^{5} + 2e^{4} - 6e^{3} - \frac{41}{3}e^{2} + \frac{28}{3}e + \frac{44}{3}$ |
89 | $[89, 89, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{4}{3}e^{6} + 7e^{5} - 5e^{4} - \frac{148}{3}e^{3} + \frac{14}{3}e^{2} + \frac{169}{3}e + 4$ |
101 | $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ | $-\frac{5}{3}e^{6} - \frac{29}{3}e^{5} + 4e^{4} + \frac{218}{3}e^{3} + \frac{31}{3}e^{2} - 98e - \frac{50}{3}$ |
101 | $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ | $-\frac{1}{3}e^{6} - \frac{8}{3}e^{5} - 2e^{4} + \frac{61}{3}e^{3} + 21e^{2} - \frac{107}{3}e - \frac{68}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, -w^{2} + 2]$ | $-1$ |