Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[45, 15, 2w^{5} - 14w^{3} - 3w^{2} + 23w + 9]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 4x^{5} - 22x^{4} + 80x^{3} + 32x^{2} - 160x + 64\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $\phantom{-}1$ |
9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $\phantom{-}1$ |
11 | $[11, 11, w - 1]$ | $\phantom{-}e$ |
25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}\frac{1}{48}e^{5} - \frac{1}{8}e^{4} - \frac{11}{24}e^{3} + \frac{37}{12}e^{2} + e - \frac{16}{3}$ |
29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $-\frac{1}{2}e^{2} + 8$ |
41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-\frac{1}{6}e^{5} + \frac{1}{2}e^{4} + \frac{25}{6}e^{3} - \frac{55}{6}e^{2} - 13e + \frac{32}{3}$ |
49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $\phantom{-}\frac{1}{48}e^{5} - \frac{1}{8}e^{4} - \frac{11}{24}e^{3} + \frac{31}{12}e^{2} + e - \frac{10}{3}$ |
59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $-\frac{1}{8}e^{5} + \frac{1}{2}e^{4} + \frac{11}{4}e^{3} - 9e^{2} - 5e + 10$ |
59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $-\frac{5}{16}e^{5} + \frac{7}{8}e^{4} + \frac{63}{8}e^{3} - \frac{65}{4}e^{2} - 26e + 28$ |
61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $\phantom{-}\frac{1}{24}e^{5} - \frac{1}{4}e^{4} - \frac{11}{12}e^{3} + \frac{17}{3}e^{2} + e - \frac{32}{3}$ |
61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $\phantom{-}\frac{1}{24}e^{5} - \frac{17}{12}e^{3} - \frac{1}{3}e^{2} + 10e - \frac{8}{3}$ |
64 | $[64, 2, 2]$ | $\phantom{-}\frac{1}{48}e^{5} - \frac{11}{24}e^{3} - \frac{1}{6}e^{2} - e + \frac{5}{3}$ |
71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $-\frac{1}{4}e^{5} + \frac{3}{4}e^{4} + \frac{13}{2}e^{3} - \frac{29}{2}e^{2} - 27e + 26$ |
71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $\phantom{-}\frac{1}{3}e^{5} - e^{4} - \frac{47}{6}e^{3} + \frac{107}{6}e^{2} + 20e - \frac{64}{3}$ |
79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{1}{2}e^{4} - \frac{25}{6}e^{3} + \frac{26}{3}e^{2} + 13e - \frac{14}{3}$ |
81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $\phantom{-}\frac{5}{48}e^{5} - \frac{3}{8}e^{4} - \frac{55}{24}e^{3} + \frac{83}{12}e^{2} + 6e - \frac{14}{3}$ |
89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $-\frac{5}{24}e^{5} + \frac{1}{2}e^{4} + \frac{61}{12}e^{3} - \frac{47}{6}e^{2} - 16e + \frac{22}{3}$ |
89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{1}{4}e^{4} - \frac{7}{3}e^{3} + \frac{29}{6}e^{2} + 14e - \frac{34}{3}$ |
89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $-e + 8$ |
89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $\phantom{-}\frac{1}{48}e^{5} + \frac{1}{8}e^{4} - \frac{23}{24}e^{3} - \frac{35}{12}e^{2} + 7e + \frac{26}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $-1$ |
$9$ | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $-1$ |