Base field 4.4.13025.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 3x + 29\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 10, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{11}{2}]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 13x^{4} + 16x^{3} + 41x^{2} - 22x - 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + w + 8]$ | $-1$ |
| 5 | $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ | $-1$ |
| 5 | $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ | $-\frac{1}{10}e^{5} + \frac{2}{5}e^{4} + e^{3} - \frac{18}{5}e^{2} - \frac{19}{10}e + 4$ |
| 19 | $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ | $-e^{2} + 2e + 5$ |
| 19 | $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{3}{10}e^{4} - 2e^{3} + \frac{6}{5}e^{2} + \frac{9}{5}e + \frac{5}{2}$ |
| 29 | $[29, 29, w]$ | $-2e$ |
| 29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ | $-\frac{1}{10}e^{5} + \frac{2}{5}e^{4} + e^{3} - \frac{23}{5}e^{2} - \frac{19}{10}e + 5$ |
| 29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ | $-e^{2} + 5$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ | $-\frac{1}{2}e^{4} + e^{3} + 5e^{2} - 5e - \frac{15}{2}$ |
| 41 | $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - e^{3} + \frac{26}{5}e^{2} - \frac{6}{5}e - 2$ |
| 41 | $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ | $\phantom{-}\frac{2}{5}e^{5} - \frac{3}{5}e^{4} - 5e^{3} + \frac{17}{5}e^{2} + \frac{63}{5}e - 2$ |
| 61 | $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ | $\phantom{-}\frac{2}{5}e^{5} - \frac{8}{5}e^{4} - 3e^{3} + \frac{67}{5}e^{2} + \frac{23}{5}e - 17$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{1}{5}e^{4} - 3e^{3} - \frac{24}{5}e^{2} + \frac{44}{5}e + 13$ |
| 79 | $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{1}{5}e^{4} - 4e^{3} - \frac{9}{5}e^{2} + \frac{79}{5}e$ |
| 79 | $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ | $-\frac{1}{5}e^{5} - \frac{1}{5}e^{4} + 4e^{3} + \frac{14}{5}e^{2} - \frac{79}{5}e - 5$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{5}e^{5} + \frac{4}{5}e^{4} + 2e^{3} - \frac{41}{5}e^{2} - \frac{19}{5}e + 13$ |
| 89 | $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ | $-\frac{1}{10}e^{5} + \frac{2}{5}e^{4} - \frac{13}{5}e^{2} + \frac{31}{10}e + 5$ |
| 89 | $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - e^{3} + \frac{31}{5}e^{2} - \frac{6}{5}e - 5$ |
| 109 | $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ | $\phantom{-}\frac{2}{5}e^{5} - \frac{3}{5}e^{4} - 6e^{3} + \frac{22}{5}e^{2} + \frac{118}{5}e - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w^{2} + w + 8]$ | $1$ |
| $5$ | $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ | $1$ |