Base field 3.3.469.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[17, 17, w + 3]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} - 2x^{6} - 9x^{5} + 13x^{4} + 25x^{3} - 17x^{2} - 16x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{1}{2}e^{4} - \frac{7}{2}e^{3} + \frac{3}{2}e^{2} + \frac{11}{2}e + \frac{1}{2}$ |
7 | $[7, 7, w + 1]$ | $-\frac{1}{2}e^{6} + e^{5} + 4e^{4} - 6e^{3} - 8e^{2} + 5e + \frac{1}{2}$ |
7 | $[7, 7, -w + 3]$ | $-e^{4} + e^{3} + 5e^{2} - 2e - 1$ |
11 | $[11, 11, -w^{2} + 3]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{5}{2}e^{3} - \frac{3}{2}e^{2} + \frac{1}{2}e + \frac{3}{2}$ |
17 | $[17, 17, w + 3]$ | $\phantom{-}1$ |
19 | $[19, 19, w^{2} - 7]$ | $-e^{6} + \frac{5}{2}e^{5} + \frac{13}{2}e^{4} - \frac{29}{2}e^{3} - \frac{23}{2}e^{2} + \frac{31}{2}e + \frac{7}{2}$ |
27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - 3e^{4} + 5e^{3} + 3e^{2} - 5e + \frac{5}{2}$ |
43 | $[43, 43, -2w - 5]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + \frac{11}{2}e^{4} - \frac{7}{2}e^{3} - \frac{33}{2}e^{2} + \frac{11}{2}e + 8$ |
47 | $[47, 47, 2w + 3]$ | $-\frac{1}{2}e^{5} + \frac{5}{2}e^{4} + \frac{5}{2}e^{3} - \frac{27}{2}e^{2} - \frac{15}{2}e + \frac{15}{2}$ |
53 | $[53, 53, 3w^{2} + 2w - 9]$ | $-e^{5} + e^{4} + 9e^{3} - 5e^{2} - 19e + 3$ |
59 | $[59, 59, 2w^{2} + w - 5]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{7}{2}e^{4} - \frac{15}{2}e^{3} + \frac{29}{2}e^{2} + \frac{13}{2}e - \frac{9}{2}$ |
61 | $[61, 61, 3w - 1]$ | $-e^{6} + 2e^{5} + 8e^{4} - 12e^{3} - 18e^{2} + 14e + 5$ |
61 | $[61, 61, 2w^{2} + w - 9]$ | $-\frac{1}{2}e^{6} + 7e^{4} - e^{3} - 25e^{2} + \frac{31}{2}$ |
61 | $[61, 61, 2w^{2} - w - 7]$ | $\phantom{-}e^{6} - 2e^{5} - 7e^{4} + 14e^{3} + 9e^{2} - 24e - 1$ |
67 | $[67, 67, -2w^{2} + 13]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - 2e^{4} + 4e^{3} - 2e^{2} - 3e + \frac{7}{2}$ |
67 | $[67, 67, -3w - 7]$ | $-\frac{1}{2}e^{6} + 2e^{5} + e^{4} - 13e^{3} + 7e^{2} + 22e - \frac{17}{2}$ |
73 | $[73, 73, w^{2} + 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{3}{2}e^{5} - \frac{7}{2}e^{4} + \frac{21}{2}e^{3} + \frac{17}{2}e^{2} - \frac{37}{2}e - 7$ |
79 | $[79, 79, w - 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{3}{2}e^{5} - \frac{7}{2}e^{4} + \frac{21}{2}e^{3} + \frac{13}{2}e^{2} - \frac{29}{2}e + 5$ |
83 | $[83, 83, -2w^{2} + 4w + 3]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + \frac{11}{2}e^{4} - \frac{3}{2}e^{3} - \frac{41}{2}e^{2} - \frac{13}{2}e + 18$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, w + 3]$ | $-1$ |