Base field 4.4.15188.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[86, 86, \frac{1}{2}w^{3} - 2w^{2} - \frac{1}{2}w + 2]$ |
| Dimension: | $38$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $118$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{38} - 2x^{37} - 59x^{36} + 117x^{35} + 1587x^{34} - 3115x^{33} - 25794x^{32} + 50000x^{31} + 283088x^{30} - 540335x^{29} - 2220932x^{28} + 4157848x^{27} + 12863785x^{26} - 23496951x^{25} - 56027906x^{24} + 99141287x^{23} + 185222851x^{22} - 314406388x^{21} - 465977305x^{20} + 748513023x^{19} + 889309006x^{18} - 1326352996x^{17} - 1276351688x^{16} + 1720618926x^{15} + 1357125865x^{14} - 1591471118x^{13} - 1044976302x^{12} + 1008163188x^{11} + 563520568x^{10} - 411097200x^{9} - 202628349x^{8} + 97413436x^{7} + 45004945x^{6} - 10990202x^{5} - 5380546x^{4} + 274027x^{3} + 255920x^{2} + 24575x + 641\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $\phantom{-}1$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $...$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 6w + 1]$ | $...$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $...$ |
| 19 | $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ | $...$ |
| 23 | $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ | $...$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w - 1]$ | $...$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $...$ |
| 43 | $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ | $\phantom{-}1$ |
| 67 | $[67, 67, w^{2} - w - 5]$ | $...$ |
| 67 | $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ | $...$ |
| 73 | $[73, 73, w^{2} + w + 1]$ | $...$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ | $...$ |
| 81 | $[81, 3, -3]$ | $...$ |
| 83 | $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ | $...$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ | $...$ |
| 89 | $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ | $...$ |
| 89 | $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ | $...$ |
| 97 | $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $-1$ |
| $43$ | $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ | $-1$ |