Base field 6.6.1134389.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 6x^{3} + 4x^{2} - 3x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - x^{7} - 25x^{6} - 14x^{5} + 129x^{4} + 160x^{3} - 85x^{2} - 164x - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{1579}{1502}e^{7} + \frac{3493}{1502}e^{6} + \frac{35259}{1502}e^{5} - \frac{10361}{751}e^{4} - \frac{178897}{1502}e^{3} - \frac{17380}{751}e^{2} + \frac{177299}{1502}e + \frac{24306}{751}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 3w]$ | $-\frac{4249}{1502}e^{7} + \frac{10735}{1502}e^{6} + \frac{90003}{1502}e^{5} - \frac{39075}{751}e^{4} - \frac{432611}{1502}e^{3} - \frac{9796}{751}e^{2} + \frac{406149}{1502}e + \frac{42702}{751}$ |
| 19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{1261}{751}e^{7} - \frac{2995}{751}e^{6} - \frac{27350}{751}e^{5} + \frac{19762}{751}e^{4} + \frac{134380}{751}e^{3} + \frac{18983}{751}e^{2} - \frac{127268}{751}e - \frac{31836}{751}$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}\frac{436}{751}e^{7} - \frac{867}{751}e^{6} - \frac{10055}{751}e^{5} + \frac{4051}{751}e^{4} + \frac{51783}{751}e^{3} + \frac{15510}{751}e^{2} - \frac{47738}{751}e - \frac{15236}{751}$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ | $-\frac{1137}{751}e^{7} + \frac{2900}{751}e^{6} + \frac{23822}{751}e^{5} - \frac{20918}{751}e^{4} - \frac{111750}{751}e^{3} - \frac{6993}{751}e^{2} + \frac{97741}{751}e + \frac{23424}{751}$ |
| 31 | $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ | $-1$ |
| 37 | $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $-\frac{2064}{751}e^{7} + \frac{4876}{751}e^{6} + \frac{45085}{751}e^{5} - \frac{32771}{751}e^{4} - \frac{224227}{751}e^{3} - \frac{24326}{751}e^{2} + \frac{218045}{751}e + \frac{45490}{751}$ |
| 37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ | $\phantom{-}\frac{4513}{1502}e^{7} - \frac{10695}{1502}e^{6} - \frac{98241}{1502}e^{5} + \frac{35761}{751}e^{4} + \frac{485297}{1502}e^{3} + \frac{28616}{751}e^{2} - \frac{463441}{1502}e - \frac{51366}{751}$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + w - 3]$ | $-\frac{3429}{751}e^{7} + \frac{8629}{751}e^{6} + \frac{72608}{751}e^{5} - \frac{62029}{751}e^{4} - \frac{347547}{751}e^{3} - \frac{22453}{751}e^{2} + \frac{323346}{751}e + \frac{76096}{751}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{1107}{751}e^{7} - \frac{2768}{751}e^{6} - \frac{23671}{751}e^{5} + \frac{20374}{751}e^{4} + \frac{115287}{751}e^{3} + \frac{2784}{751}e^{2} - \frac{110620}{751}e - \frac{20977}{751}$ |
| 67 | $[67, 67, 2w - 1]$ | $-\frac{4479}{751}e^{7} + \frac{10996}{751}e^{6} + \frac{95917}{751}e^{5} - \frac{76563}{751}e^{4} - \frac{465574}{751}e^{3} - \frac{42849}{751}e^{2} + \frac{439586}{751}e + \frac{102412}{751}$ |
| 79 | $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ | $-\frac{524}{751}e^{7} + \frac{1104}{751}e^{6} + \frac{12050}{751}e^{5} - \frac{6598}{751}e^{4} - \frac{63337}{751}e^{3} - \frac{8030}{751}e^{2} + \frac{65834}{751}e + \frac{12000}{751}$ |
| 79 | $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ | $-\frac{1729}{751}e^{7} + \frac{4153}{751}e^{6} + \frac{37516}{751}e^{5} - \frac{28699}{751}e^{4} - \frac{185244}{751}e^{3} - \frac{15251}{751}e^{2} + \frac{181245}{751}e + \frac{42072}{751}$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ | $\phantom{-}\frac{4068}{751}e^{7} - \frac{10239}{751}e^{6} - \frac{86113}{751}e^{5} + \frac{73466}{751}e^{4} + \frac{411970}{751}e^{3} + \frac{28969}{751}e^{2} - \frac{379989}{751}e - \frac{95098}{751}$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ | $\phantom{-}\frac{1821}{1502}e^{7} - \frac{3957}{1502}e^{6} - \frac{40933}{1502}e^{5} + \frac{11704}{751}e^{4} + \frac{207291}{1502}e^{3} + \frac{16107}{751}e^{2} - \frac{197023}{1502}e - \frac{12722}{751}$ |
| 101 | $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ | $\phantom{-}\frac{8679}{1502}e^{7} - \frac{21215}{1502}e^{6} - \frac{186149}{1502}e^{5} + \frac{73733}{751}e^{4} + \frac{902385}{1502}e^{3} + \frac{37809}{751}e^{2} - \frac{842213}{1502}e - \frac{85814}{751}$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ | $\phantom{-}\frac{4293}{1502}e^{7} - \frac{9727}{1502}e^{6} - \frac{95131}{1502}e^{5} + \frac{30512}{751}e^{4} + \frac{478191}{1502}e^{3} + \frac{35713}{751}e^{2} - \frac{464763}{1502}e - \frac{47150}{751}$ |
| 103 | $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ | $\phantom{-}\frac{1293}{751}e^{7} - \frac{3286}{751}e^{6} - \frac{27461}{751}e^{5} + \frac{24648}{751}e^{4} + \frac{133461}{751}e^{3} - \frac{259}{751}e^{2} - \frac{135009}{751}e - \frac{17824}{751}$ |
| 107 | $[107, 107, w^{2} - 2w - 3]$ | $-\frac{3933}{751}e^{7} + \frac{9645}{751}e^{6} + \frac{84307}{751}e^{5} - \frac{67263}{751}e^{4} - \frac{409487}{751}e^{3} - \frac{37440}{751}e^{2} + \frac{385750}{751}e + \frac{91972}{751}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31,31,w^{5}-2w^{4}-4w^{3}+5w^{2}+5w-1]$ | $1$ |