Base field 4.4.17069.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} - 4x + 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[17, 17, w^{3} - w^{2} - 8w - 5]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 13x^{4} - 2x^{3} + 40x^{2} + 21x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}\frac{4}{19}e^{5} + \frac{3}{19}e^{4} - \frac{45}{19}e^{3} - \frac{18}{19}e^{2} + \frac{99}{19}e + \frac{11}{19}$ |
3 | $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ | $\phantom{-}\frac{2}{19}e^{5} - \frac{8}{19}e^{4} - \frac{32}{19}e^{3} + \frac{67}{19}e^{2} + \frac{97}{19}e - \frac{23}{19}$ |
16 | $[16, 2, 2]$ | $-\frac{5}{19}e^{5} + \frac{1}{19}e^{4} + \frac{61}{19}e^{3} - \frac{25}{19}e^{2} - \frac{157}{19}e + \frac{29}{19}$ |
17 | $[17, 17, w^{3} - w^{2} - 8w - 5]$ | $\phantom{-}1$ |
17 | $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ | $-\frac{2}{19}e^{5} + \frac{8}{19}e^{4} + \frac{32}{19}e^{3} - \frac{67}{19}e^{2} - \frac{97}{19}e - \frac{15}{19}$ |
17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{6}{19}e^{5} + \frac{5}{19}e^{4} + \frac{58}{19}e^{3} - \frac{68}{19}e^{2} - \frac{82}{19}e + \frac{69}{19}$ |
17 | $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}\frac{2}{19}e^{5} - \frac{8}{19}e^{4} - \frac{32}{19}e^{3} + \frac{67}{19}e^{2} + \frac{97}{19}e - \frac{61}{19}$ |
25 | $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ | $\phantom{-}\frac{2}{19}e^{5} + \frac{11}{19}e^{4} - \frac{13}{19}e^{3} - \frac{85}{19}e^{2} - \frac{17}{19}e + \frac{34}{19}$ |
25 | $[25, 5, w^{2} - 2w - 7]$ | $-\frac{12}{19}e^{5} - \frac{9}{19}e^{4} + \frac{116}{19}e^{3} + \frac{54}{19}e^{2} - \frac{183}{19}e + \frac{5}{19}$ |
29 | $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{5}{19}e^{5} - \frac{1}{19}e^{4} - \frac{23}{19}e^{3} + \frac{25}{19}e^{2} - \frac{90}{19}e - \frac{86}{19}$ |
29 | $[29, 29, w - 2]$ | $-\frac{6}{19}e^{5} + \frac{5}{19}e^{4} + \frac{77}{19}e^{3} - \frac{30}{19}e^{2} - \frac{196}{19}e - \frac{45}{19}$ |
53 | $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ | $-\frac{5}{19}e^{5} + \frac{1}{19}e^{4} + \frac{42}{19}e^{3} - \frac{6}{19}e^{2} - \frac{5}{19}e - \frac{104}{19}$ |
53 | $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ | $\phantom{-}\frac{10}{19}e^{5} - \frac{2}{19}e^{4} - \frac{122}{19}e^{3} - \frac{7}{19}e^{2} + \frac{333}{19}e + \frac{189}{19}$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ | $-\frac{10}{19}e^{5} + \frac{40}{19}e^{4} + \frac{141}{19}e^{3} - \frac{335}{19}e^{2} - \frac{447}{19}e + \frac{210}{19}$ |
61 | $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ | $\phantom{-}\frac{6}{19}e^{5} + \frac{14}{19}e^{4} - \frac{58}{19}e^{3} - \frac{103}{19}e^{2} + \frac{101}{19}e - \frac{12}{19}$ |
101 | $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ | $\phantom{-}\frac{4}{19}e^{5} + \frac{3}{19}e^{4} - \frac{7}{19}e^{3} + \frac{58}{19}e^{2} - \frac{186}{19}e - \frac{274}{19}$ |
103 | $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ | $-\frac{2}{19}e^{5} + \frac{27}{19}e^{4} + \frac{51}{19}e^{3} - \frac{200}{19}e^{2} - \frac{211}{19}e + \frac{4}{19}$ |
103 | $[103, 103, -w^{3} + w^{2} + 8w + 2]$ | $\phantom{-}\frac{2}{19}e^{5} + \frac{11}{19}e^{4} + \frac{6}{19}e^{3} - \frac{123}{19}e^{2} - \frac{131}{19}e + \frac{262}{19}$ |
113 | $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}\frac{16}{19}e^{5} - \frac{26}{19}e^{4} - \frac{199}{19}e^{3} + \frac{213}{19}e^{2} + \frac{510}{19}e - \frac{203}{19}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, w^{3} - w^{2} - 8w - 5]$ | $-1$ |