Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[11, 11, w^{3} - w^{2} - 4w + 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + x^{4} - 17x^{3} - 12x^{2} + 62x + 53\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{2}{31}e^{4} - \frac{3}{31}e^{3} - \frac{42}{31}e^{2} + \frac{50}{31}e + \frac{185}{31}$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-1$ |
13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $\phantom{-}0$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{5}{62}e^{4} + \frac{4}{31}e^{3} - \frac{43}{62}e^{2} - \frac{61}{62}e + \frac{13}{62}$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{9}{31}e^{4} - \frac{2}{31}e^{3} + \frac{127}{31}e^{2} - \frac{8}{31}e - \frac{228}{31}$ |
19 | $[19, 19, w^{3} - 5w]$ | $-\frac{4}{31}e^{4} + \frac{6}{31}e^{3} + \frac{53}{31}e^{2} - \frac{69}{31}e - \frac{60}{31}$ |
19 | $[19, 19, -w + 3]$ | $\phantom{-}\frac{8}{31}e^{4} - \frac{12}{31}e^{3} - \frac{137}{31}e^{2} + \frac{169}{31}e + \frac{430}{31}$ |
23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $-\frac{1}{31}e^{4} + \frac{17}{31}e^{3} + \frac{52}{31}e^{2} - \frac{180}{31}e - \frac{232}{31}$ |
23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}\frac{13}{31}e^{4} + \frac{27}{31}e^{3} - \frac{149}{31}e^{2} - \frac{171}{31}e + \frac{226}{31}$ |
25 | $[25, 5, w^{2} - 3]$ | $-\frac{7}{31}e^{4} - \frac{5}{31}e^{3} + \frac{85}{31}e^{2} + \frac{42}{31}e - \frac{105}{31}$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $-\frac{3}{31}e^{4} - \frac{11}{31}e^{3} + \frac{32}{31}e^{2} + \frac{49}{31}e + \frac{79}{31}$ |
37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $-\frac{27}{62}e^{4} - \frac{34}{31}e^{3} + \frac{319}{62}e^{2} + \frac{503}{62}e - \frac{405}{62}$ |
41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{10}{31}e^{4} - \frac{16}{31}e^{3} + \frac{117}{31}e^{2} + \frac{60}{31}e + \frac{5}{31}$ |
47 | $[47, 47, w^{3} - 6w + 1]$ | $\phantom{-}\frac{16}{31}e^{4} + \frac{38}{31}e^{3} - \frac{150}{31}e^{2} - \frac{251}{31}e - \frac{70}{31}$ |
61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{12}{31}e^{4} + \frac{13}{31}e^{3} - \frac{159}{31}e^{2} - \frac{134}{31}e + \frac{304}{31}$ |
67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $\phantom{-}\frac{1}{31}e^{4} + \frac{45}{31}e^{3} + \frac{72}{31}e^{2} - \frac{409}{31}e - \frac{481}{31}$ |
67 | $[67, 67, w^{3} - 7w + 3]$ | $-\frac{13}{62}e^{4} - \frac{29}{31}e^{3} + \frac{25}{62}e^{2} + \frac{605}{62}e + \frac{487}{62}$ |
73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $\phantom{-}\frac{24}{31}e^{4} + \frac{26}{31}e^{3} - \frac{287}{31}e^{2} - \frac{144}{31}e + \frac{484}{31}$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{2}{31}e^{4} - \frac{34}{31}e^{3} - \frac{135}{31}e^{2} + \frac{329}{31}e + \frac{650}{31}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $1$ |