Base field 6.6.1868969.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 8x^{2} + x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[34, 34, -w^{5} + w^{4} + 4w^{3} - 3w^{2} - 2w + 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 16x^{4} + 80x^{3} + 87x^{2} - 243x - 266\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $-1$ |
| 23 | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-\frac{1}{5}e^{4} - \frac{12}{5}e^{3} - \frac{32}{5}e^{2} + \frac{31}{5}e + \frac{54}{5}$ |
| 31 | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ | $\phantom{-}\frac{29}{25}e^{4} + \frac{308}{25}e^{3} + \frac{658}{25}e^{2} - \frac{1089}{25}e - \frac{1426}{25}$ |
| 32 | $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ | $\phantom{-}\frac{4}{25}e^{4} + \frac{33}{25}e^{3} + \frac{33}{25}e^{2} - \frac{114}{25}e + \frac{49}{25}$ |
| 43 | $[43, 43, w^{4} - 5w^{2} + 3]$ | $\phantom{-}\frac{4}{25}e^{4} + \frac{58}{25}e^{3} + \frac{183}{25}e^{2} - \frac{189}{25}e - \frac{526}{25}$ |
| 47 | $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ | $-\frac{13}{25}e^{4} - \frac{126}{25}e^{3} - \frac{226}{25}e^{2} + \frac{433}{25}e + \frac{322}{25}$ |
| 49 | $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ | $-\frac{6}{25}e^{4} - \frac{62}{25}e^{3} - \frac{137}{25}e^{2} + \frac{171}{25}e + \frac{264}{25}$ |
| 53 | $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ | $\phantom{-}\frac{26}{25}e^{4} + \frac{277}{25}e^{3} + \frac{577}{25}e^{2} - \frac{1041}{25}e - \frac{1244}{25}$ |
| 59 | $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{6}{25}e^{4} + \frac{62}{25}e^{3} + \frac{137}{25}e^{2} - \frac{196}{25}e - \frac{464}{25}$ |
| 71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ | $-\frac{46}{25}e^{4} - \frac{492}{25}e^{3} - \frac{1067}{25}e^{2} + \frac{1736}{25}e + \frac{2324}{25}$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $-\frac{32}{25}e^{4} - \frac{339}{25}e^{3} - \frac{714}{25}e^{2} + \frac{1212}{25}e + \frac{1408}{25}$ |
| 83 | $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ | $-\frac{26}{25}e^{4} - \frac{277}{25}e^{3} - \frac{577}{25}e^{2} + \frac{1041}{25}e + \frac{1094}{25}$ |
| 83 | $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ | $-\frac{21}{25}e^{4} - \frac{242}{25}e^{3} - \frac{617}{25}e^{2} + \frac{636}{25}e + \frac{1324}{25}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ | $\phantom{-}\frac{19}{25}e^{4} + \frac{213}{25}e^{3} + \frac{488}{25}e^{2} - \frac{779}{25}e - \frac{1036}{25}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ | $\phantom{-}\frac{4}{5}e^{4} + \frac{43}{5}e^{3} + \frac{98}{5}e^{2} - \frac{149}{5}e - \frac{296}{5}$ |
| 89 | $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ | $\phantom{-}\frac{16}{25}e^{4} + \frac{182}{25}e^{3} + \frac{407}{25}e^{2} - \frac{781}{25}e - \frac{1004}{25}$ |
| 89 | $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ | $-\frac{6}{25}e^{4} - \frac{62}{25}e^{3} - \frac{162}{25}e^{2} + \frac{71}{25}e + \frac{564}{25}$ |
| 101 | $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ | $-\frac{51}{25}e^{4} - \frac{527}{25}e^{3} - \frac{1052}{25}e^{2} + \frac{2016}{25}e + \frac{2294}{25}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w]$ | $-1$ |
| $17$ | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $1$ |