Base field 6.6.1416125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 9x^{3} + 6x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{3} + 4w + 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 6x^{7} + 2x^{6} - 33x^{5} - 21x^{4} + 65x^{3} + 19x^{2} - 47x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{7}{11}e^{7} - 3e^{6} + \frac{19}{11}e^{5} + \frac{172}{11}e^{4} - \frac{5}{11}e^{3} - \frac{249}{11}e^{2} - \frac{14}{11}e + \frac{72}{11}$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $\phantom{-}\frac{4}{11}e^{7} + 3e^{6} + \frac{63}{11}e^{5} - \frac{92}{11}e^{4} - \frac{291}{11}e^{3} + \frac{48}{11}e^{2} + \frac{261}{11}e - \frac{71}{11}$ |
| 19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ | $\phantom{-}\frac{3}{11}e^{7} + e^{6} - \frac{27}{11}e^{5} - \frac{80}{11}e^{4} + \frac{98}{11}e^{3} + \frac{146}{11}e^{2} - \frac{137}{11}e - \frac{23}{11}$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ | $-\frac{20}{11}e^{7} - 8e^{6} + \frac{70}{11}e^{5} + \frac{405}{11}e^{4} - \frac{162}{11}e^{3} - \frac{427}{11}e^{2} + \frac{224}{11}e - \frac{8}{11}$ |
| 25 | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $-\frac{2}{11}e^{7} + 3e^{6} + \frac{194}{11}e^{5} - \frac{86}{11}e^{4} - \frac{850}{11}e^{3} + \frac{185}{11}e^{2} + \frac{832}{11}e - \frac{278}{11}$ |
| 29 | $[29, 29, -w^{3} + 4w + 1]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $\phantom{-}\frac{12}{11}e^{7} + 4e^{6} - \frac{86}{11}e^{5} - \frac{243}{11}e^{4} + \frac{260}{11}e^{3} + \frac{320}{11}e^{2} - \frac{218}{11}e - \frac{81}{11}$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ | $\phantom{-}\frac{17}{11}e^{7} + 5e^{6} - \frac{164}{11}e^{5} - \frac{358}{11}e^{4} + \frac{548}{11}e^{3} + \frac{512}{11}e^{2} - \frac{527}{11}e - \frac{2}{11}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ | $-\frac{14}{11}e^{7} - 4e^{6} + \frac{126}{11}e^{5} + \frac{212}{11}e^{4} - \frac{505}{11}e^{3} - \frac{157}{11}e^{2} + \frac{588}{11}e - \frac{186}{11}$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 2w - 3]$ | $-\frac{8}{11}e^{7} - 5e^{6} - \frac{49}{11}e^{5} + \frac{283}{11}e^{4} + \frac{351}{11}e^{3} - \frac{470}{11}e^{2} - \frac{390}{11}e + \frac{252}{11}$ |
| 61 | $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ | $-\frac{30}{11}e^{7} - 16e^{6} - \frac{104}{11}e^{5} + \frac{679}{11}e^{4} + \frac{637}{11}e^{3} - \frac{668}{11}e^{2} - \frac{511}{11}e + \frac{142}{11}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{13}{11}e^{7} + 3e^{6} - \frac{161}{11}e^{5} - \frac{222}{11}e^{4} + \frac{586}{11}e^{3} + \frac{178}{11}e^{2} - \frac{623}{11}e + \frac{256}{11}$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $\phantom{-}\frac{25}{11}e^{7} + 4e^{6} - \frac{401}{11}e^{5} - \frac{388}{11}e^{4} + \frac{1561}{11}e^{3} + \frac{465}{11}e^{2} - \frac{1622}{11}e + \frac{318}{11}$ |
| 71 | $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ | $\phantom{-}\frac{16}{11}e^{7} + 8e^{6} + \frac{32}{11}e^{5} - \frac{335}{11}e^{4} - \frac{229}{11}e^{3} + \frac{324}{11}e^{2} + \frac{142}{11}e - \frac{108}{11}$ |
| 79 | $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ | $-\frac{15}{11}e^{7} - 2e^{6} + \frac{267}{11}e^{5} + \frac{257}{11}e^{4} - \frac{996}{11}e^{3} - \frac{323}{11}e^{2} + \frac{1015}{11}e - \frac{248}{11}$ |
| 79 | $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ | $-\frac{30}{11}e^{7} - 11e^{6} + \frac{160}{11}e^{5} + \frac{613}{11}e^{4} - \frac{408}{11}e^{3} - \frac{679}{11}e^{2} + \frac{336}{11}e + \frac{10}{11}$ |
| 89 | $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ | $\phantom{-}\frac{17}{11}e^{7} + 4e^{6} - \frac{219}{11}e^{5} - \frac{369}{11}e^{4} + \frac{702}{11}e^{3} + \frac{567}{11}e^{2} - \frac{582}{11}e - \frac{57}{11}$ |
| 109 | $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ | $-\frac{52}{11}e^{7} - 21e^{6} + \frac{171}{11}e^{5} + \frac{1042}{11}e^{4} - \frac{419}{11}e^{3} - \frac{1086}{11}e^{2} + \frac{611}{11}e - \frac{56}{11}$ |
| 109 | $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ | $\phantom{-}\frac{9}{11}e^{7} + 3e^{6} - \frac{70}{11}e^{5} - \frac{218}{11}e^{4} + \frac{151}{11}e^{3} + \frac{306}{11}e^{2} - \frac{70}{11}e - \frac{14}{11}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{3} + 4w + 1]$ | $-1$ |