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: | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} - 6x^{6} - 6x^{5} + 88x^{4} - 103x^{3} - 138x^{2} + 144x + 112\) |
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 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ | $-\frac{1}{4}e^{6} + \frac{5}{4}e^{5} + \frac{5}{2}e^{4} - \frac{71}{4}e^{3} + \frac{41}{4}e^{2} + \frac{39}{2}e$ |
25 | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{8}e^{5} - \frac{25}{8}e^{4} + \frac{23}{8}e^{3} + \frac{85}{4}e^{2} - 18e - 22$ |
29 | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $-\frac{1}{4}e^{6} + e^{5} + \frac{13}{4}e^{4} - \frac{29}{2}e^{3} - e^{2} + 21e + 12$ |
31 | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $-1$ |
31 | $[31, 31, -w^{2} + 2]$ | $-\frac{1}{4}e^{6} + \frac{3}{4}e^{5} + \frac{17}{4}e^{4} - \frac{45}{4}e^{3} - \frac{29}{2}e^{2} + 22e + 24$ |
59 | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{9}{4}e^{5} - \frac{21}{4}e^{4} + \frac{125}{4}e^{3} - \frac{67}{4}e^{2} - \frac{55}{2}e + 2$ |
59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ | $-\frac{1}{2}e^{5} + \frac{3}{2}e^{4} + \frac{13}{2}e^{3} - \frac{41}{2}e^{2} - e + 16$ |
59 | $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{1}{2}e^{5} - \frac{9}{2}e^{4} + 7e^{3} + \frac{65}{4}e^{2} - \frac{19}{2}e - 12$ |
61 | $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ | $\phantom{-}\frac{1}{4}e^{6} - 2e^{5} + e^{4} + \frac{51}{2}e^{3} - \frac{237}{4}e^{2} + \frac{11}{2}e + 54$ |
64 | $[64, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{4}e^{5} - \frac{9}{4}e^{4} + \frac{71}{4}e^{3} - \frac{27}{2}e^{2} - 17e - 1$ |
71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{5}{2}e^{4} - \frac{39}{4}e^{3} + 35e^{2} - e - 36$ |
71 | $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ | $-\frac{1}{8}e^{6} + \frac{5}{8}e^{5} + \frac{5}{8}e^{4} - \frac{59}{8}e^{3} + \frac{61}{4}e^{2} - 10e - 14$ |
71 | $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ | $-\frac{1}{4}e^{6} + e^{5} + 3e^{4} - \frac{29}{2}e^{3} + \frac{13}{4}e^{2} + \frac{37}{2}e + 8$ |
71 | $[71, 71, w^{3} - 5w]$ | $\phantom{-}\frac{1}{8}e^{6} + \frac{5}{8}e^{5} - \frac{49}{8}e^{4} - \frac{47}{8}e^{3} + \frac{251}{4}e^{2} - 32e - 64$ |
79 | $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}\frac{1}{2}e^{6} - 2e^{5} - \frac{27}{4}e^{4} + 30e^{3} + \frac{13}{4}e^{2} - \frac{103}{2}e - 12$ |
89 | $[89, 89, w^{3} - w^{2} - 4w + 1]$ | $-\frac{5}{8}e^{6} + \frac{19}{8}e^{5} + \frac{65}{8}e^{4} - \frac{273}{8}e^{3} - \frac{1}{4}e^{2} + 47e + 14$ |
101 | $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ | $\phantom{-}e^{5} - 4e^{4} - 12e^{3} + 56e^{2} - 14e - 54$ |
101 | $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ | $\phantom{-}\frac{5}{8}e^{6} - \frac{27}{8}e^{5} - \frac{25}{8}e^{4} + \frac{353}{8}e^{3} - \frac{279}{4}e^{2} - 7e + 58$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $1$ |