Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} + 2x^{5} - 22x^{4} - 50x^{3} + 93x^{2} + 213x - 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{2} - 2w - 6]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -w^{2} + 7]$ | $-1$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $\phantom{-}e$ |
| 5 | $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ | $\phantom{-}\frac{33}{199}e^{5} - \frac{15}{199}e^{4} - \frac{653}{199}e^{3} - \frac{11}{199}e^{2} + \frac{2499}{199}e + \frac{81}{199}$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ | $-\frac{13}{199}e^{5} + \frac{24}{199}e^{4} + \frac{209}{199}e^{3} - \frac{261}{199}e^{2} - \frac{695}{199}e + \frac{348}{199}$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ | $-\frac{20}{199}e^{5} - \frac{9}{199}e^{4} + \frac{444}{199}e^{3} + \frac{272}{199}e^{2} - \frac{2003}{199}e - \frac{827}{199}$ |
| 31 | $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ | $-\frac{53}{199}e^{5} + \frac{6}{199}e^{4} + \frac{1097}{199}e^{3} + \frac{84}{199}e^{2} - \frac{4303}{199}e + \frac{286}{199}$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $-\frac{101}{199}e^{5} + \frac{64}{199}e^{4} + \frac{2083}{199}e^{3} - \frac{298}{199}e^{2} - \frac{8951}{199}e + \frac{530}{199}$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ | $\phantom{-}e^{2} - e - 12$ |
| 41 | $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ | $\phantom{-}\frac{88}{199}e^{5} - \frac{40}{199}e^{4} - \frac{1874}{199}e^{3} + \frac{236}{199}e^{2} + \frac{8057}{199}e - \frac{1575}{199}$ |
| 41 | $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ | $-\frac{114}{199}e^{5} + \frac{88}{199}e^{4} + \frac{2292}{199}e^{3} - \frac{758}{199}e^{2} - \frac{9447}{199}e + \frac{2271}{199}$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ | $\phantom{-}\frac{48}{199}e^{5} - \frac{58}{199}e^{4} - \frac{986}{199}e^{3} + \frac{581}{199}e^{2} + \frac{4449}{199}e - \frac{642}{199}$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ | $\phantom{-}\frac{110}{199}e^{5} - \frac{50}{199}e^{4} - \frac{2243}{199}e^{3} - \frac{103}{199}e^{2} + \frac{9126}{199}e + \frac{1663}{199}$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $\phantom{-}\frac{29}{199}e^{5} + \frac{23}{199}e^{4} - \frac{604}{199}e^{3} - \frac{474}{199}e^{2} + \frac{2178}{199}e - \frac{164}{199}$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ | $\phantom{-}\frac{2}{199}e^{5} - \frac{19}{199}e^{4} + \frac{75}{199}e^{3} - \frac{67}{199}e^{2} - \frac{934}{199}e + \frac{2411}{199}$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ | $-\frac{65}{199}e^{5} + \frac{120}{199}e^{4} + \frac{1244}{199}e^{3} - \frac{1504}{199}e^{2} - \frac{5266}{199}e + \frac{2934}{199}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{118}{199}e^{5} - \frac{126}{199}e^{4} - \frac{2341}{199}e^{3} + \frac{1022}{199}e^{2} + \frac{9569}{199}e - \frac{2225}{199}$ |
| 89 | $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ | $\phantom{-}\frac{48}{199}e^{5} - \frac{58}{199}e^{4} - \frac{986}{199}e^{3} + \frac{382}{199}e^{2} + \frac{4648}{199}e - \frac{244}{199}$ |
| 89 | $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ | $-\frac{165}{199}e^{5} + \frac{75}{199}e^{4} + \frac{3265}{199}e^{3} + \frac{55}{199}e^{2} - \frac{12495}{199}e - \frac{405}{199}$ |
| 89 | $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ | $-\frac{99}{199}e^{5} + \frac{45}{199}e^{4} + \frac{1959}{199}e^{3} + \frac{33}{199}e^{2} - \frac{7895}{199}e - \frac{243}{199}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{2} - 2w - 6]$ | $-1$ |
| $4$ | $[4, 2, -w^{2} + 7]$ | $1$ |