Base field 3.3.1396.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[14, 14, w^{2} - w - 6]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 14x^{3} - 14x^{2} + 38x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{2} + 6]$ | $\phantom{-}\frac{3}{14}e^{4} + \frac{5}{7}e^{3} - \frac{19}{7}e^{2} - \frac{44}{7}e + \frac{45}{7}$ |
| 5 | $[5, 5, -w + 2]$ | $-\frac{1}{7}e^{4} - \frac{1}{7}e^{3} + \frac{15}{7}e^{2} + \frac{6}{7}e - \frac{30}{7}$ |
| 7 | $[7, 7, w + 2]$ | $-1$ |
| 11 | $[11, 11, 2w - 1]$ | $-\frac{3}{14}e^{4} - \frac{5}{7}e^{3} + \frac{12}{7}e^{2} + \frac{37}{7}e - \frac{3}{7}$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $\phantom{-}e - 2$ |
| 27 | $[27, 3, 3]$ | $-\frac{4}{7}e^{4} - \frac{11}{7}e^{3} + \frac{46}{7}e^{2} + \frac{94}{7}e - \frac{92}{7}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-\frac{6}{7}e^{4} - \frac{20}{7}e^{3} + \frac{69}{7}e^{2} + \frac{169}{7}e - \frac{138}{7}$ |
| 41 | $[41, 41, 3w^{2} - w - 23]$ | $-\frac{1}{14}e^{4} - \frac{4}{7}e^{3} + \frac{4}{7}e^{2} + \frac{31}{7}e - \frac{15}{7}$ |
| 41 | $[41, 41, w^{2} - 2]$ | $\phantom{-}\frac{5}{14}e^{4} + \frac{6}{7}e^{3} - \frac{34}{7}e^{2} - \frac{50}{7}e + \frac{33}{7}$ |
| 43 | $[43, 43, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{7}e^{4} + \frac{1}{7}e^{3} - \frac{15}{7}e^{2} - \frac{20}{7}e + \frac{16}{7}$ |
| 47 | $[47, 47, -w - 4]$ | $-\frac{11}{14}e^{4} - \frac{16}{7}e^{3} + \frac{65}{7}e^{2} + \frac{145}{7}e - \frac{123}{7}$ |
| 49 | $[49, 7, 3w^{2} - 2w - 24]$ | $\phantom{-}\frac{6}{7}e^{4} + \frac{13}{7}e^{3} - \frac{69}{7}e^{2} - \frac{99}{7}e + \frac{82}{7}$ |
| 53 | $[53, 53, 2w^{2} - w - 12]$ | $\phantom{-}\frac{9}{14}e^{4} + \frac{8}{7}e^{3} - \frac{57}{7}e^{2} - \frac{62}{7}e + \frac{93}{7}$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{9}{14}e^{4} + \frac{15}{7}e^{3} - \frac{50}{7}e^{2} - \frac{125}{7}e + \frac{93}{7}$ |
| 61 | $[61, 61, -w^{2} + 3w - 3]$ | $\phantom{-}\frac{13}{14}e^{4} + \frac{17}{7}e^{3} - \frac{80}{7}e^{2} - \frac{137}{7}e + \frac{125}{7}$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $-\frac{3}{14}e^{4} - \frac{5}{7}e^{3} + \frac{19}{7}e^{2} + \frac{37}{7}e - \frac{45}{7}$ |
| 79 | $[79, 79, 2w + 3]$ | $-\frac{9}{14}e^{4} - \frac{8}{7}e^{3} + \frac{57}{7}e^{2} + \frac{55}{7}e - \frac{107}{7}$ |
| 89 | $[89, 89, 2w - 7]$ | $-\frac{3}{14}e^{4} + \frac{2}{7}e^{3} + \frac{26}{7}e^{2} - \frac{47}{7}e - \frac{87}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 1]$ | $1$ |
| $7$ | $[7, 7, w + 2]$ | $1$ |