Base field 6.6.300125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[125, 5, 4w^{5} - w^{4} - 29w^{3} - 13w^{2} + 19w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 10x^{5} - 84x^{4} + 880x^{3} - 112x^{2} - 4224x + 1728\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 29 | $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ | $-\frac{1}{1944}e^{5} + \frac{23}{1944}e^{4} + \frac{7}{486}e^{3} - \frac{277}{243}e^{2} + \frac{152}{81}e + \frac{88}{9}$ |
| 29 | $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ | $\phantom{-}\frac{7}{1296}e^{5} - \frac{31}{648}e^{4} - \frac{157}{324}e^{3} + \frac{661}{162}e^{2} + \frac{53}{27}e - \frac{32}{3}$ |
| 29 | $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ | $\phantom{-}e$ |
| 29 | $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ | $-\frac{1}{1944}e^{5} - \frac{1}{486}e^{4} + \frac{95}{972}e^{3} + \frac{121}{486}e^{2} - \frac{388}{81}e - \frac{2}{9}$ |
| 29 | $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ | $-\frac{7}{3888}e^{5} + \frac{5}{243}e^{4} + \frac{65}{486}e^{3} - \frac{805}{486}e^{2} + \frac{100}{81}e + \frac{20}{9}$ |
| 29 | $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ | $-\frac{5}{1944}e^{5} + \frac{17}{972}e^{4} + \frac{58}{243}e^{3} - \frac{745}{486}e^{2} - \frac{104}{81}e + \frac{80}{9}$ |
| 41 | $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ | $\phantom{-}\frac{1}{1296}e^{5} - \frac{5}{1296}e^{4} - \frac{17}{162}e^{3} + \frac{26}{81}e^{2} + \frac{77}{27}e + \frac{7}{3}$ |
| 41 | $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ | $\phantom{-}\frac{1}{1296}e^{5} - \frac{7}{648}e^{4} - \frac{41}{648}e^{3} + \frac{329}{324}e^{2} - \frac{13}{27}e - \frac{8}{3}$ |
| 41 | $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ | $\phantom{-}\frac{1}{972}e^{5} - \frac{19}{1944}e^{4} - \frac{109}{972}e^{3} + \frac{433}{486}e^{2} + \frac{391}{162}e - \frac{23}{9}$ |
| 41 | $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ | $-\frac{1}{432}e^{5} + \frac{1}{54}e^{4} + \frac{25}{108}e^{3} - \frac{179}{108}e^{2} - \frac{23}{9}e + 11$ |
| 41 | $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ | $-\frac{5}{2592}e^{5} + \frac{13}{648}e^{4} + \frac{29}{162}e^{3} - \frac{557}{324}e^{2} - \frac{35}{27}e + \frac{23}{3}$ |
| 41 | $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ | $\phantom{-}\frac{13}{7776}e^{5} - \frac{55}{3888}e^{4} - \frac{253}{1944}e^{3} + \frac{1117}{972}e^{2} - \frac{151}{162}e + \frac{11}{9}$ |
| 49 | $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ | $\phantom{-}0$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}4$ |
| 71 | $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ | $\phantom{-}\frac{5}{1296}e^{5} - \frac{13}{324}e^{4} - \frac{29}{81}e^{3} + \frac{557}{162}e^{2} + \frac{167}{54}e - \frac{31}{3}$ |
| 71 | $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ | $-\frac{7}{1944}e^{5} + \frac{53}{1944}e^{4} + \frac{601}{1944}e^{3} - \frac{2113}{972}e^{2} - \frac{43}{81}e + \frac{22}{9}$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ | $-\frac{19}{7776}e^{5} + \frac{31}{972}e^{4} + \frac{47}{243}e^{3} - \frac{2779}{972}e^{2} + \frac{128}{81}e + \frac{103}{9}$ |
| 71 | $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ | $\phantom{-}\frac{17}{3888}e^{5} - \frac{121}{3888}e^{4} - \frac{443}{972}e^{3} + \frac{667}{243}e^{2} + \frac{490}{81}e - \frac{109}{9}$ |
| 71 | $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ | $\phantom{-}\frac{1}{864}e^{5} - \frac{7}{432}e^{4} - \frac{7}{216}e^{3} + \frac{151}{108}e^{2} - \frac{85}{18}e - 5$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ | $-\frac{13}{3888}e^{5} + \frac{55}{1944}e^{4} + \frac{167}{486}e^{3} - \frac{2477}{972}e^{2} - \frac{443}{81}e + \frac{131}{9}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $125$ | $[125, 5, 4w^{5} - w^{4} - 29w^{3} - 13w^{2} + 19w + 2]$ | $1$ |