Base field 6.6.1995125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 6x^{5} - 23x^{4} - 196x^{3} - 264x^{2} + 160x + 320\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ | $-\frac{19}{148}e^{5} - \frac{22}{37}e^{4} + \frac{573}{148}e^{3} + \frac{734}{37}e^{2} + \frac{283}{74}e - \frac{1051}{37}$ |
| 11 | $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{9}{296}e^{5} - \frac{15}{148}e^{4} + \frac{287}{296}e^{3} + \frac{131}{37}e^{2} - \frac{117}{74}e - \frac{246}{37}$ |
| 19 | $[19, 19, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{43}{296}e^{5} + \frac{21}{37}e^{4} - \frac{1289}{296}e^{3} - \frac{2853}{148}e^{2} - \frac{255}{74}e + \frac{830}{37}$ |
| 19 | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $\phantom{-}\frac{11}{74}e^{5} + \frac{49}{74}e^{4} - \frac{161}{37}e^{3} - \frac{1655}{74}e^{2} - \frac{501}{74}e + \frac{1104}{37}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ | $-\frac{17}{148}e^{5} - \frac{69}{148}e^{4} + \frac{501}{148}e^{3} + \frac{2329}{148}e^{2} + \frac{149}{37}e - \frac{769}{37}$ |
| 29 | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ | $\phantom{-}\frac{85}{592}e^{5} + \frac{191}{296}e^{4} - \frac{2579}{592}e^{3} - \frac{3235}{148}e^{2} - \frac{66}{37}e + \frac{1359}{37}$ |
| 29 | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $-\frac{29}{592}e^{5} - \frac{73}{296}e^{4} + \frac{859}{592}e^{3} + \frac{603}{74}e^{2} + \frac{237}{74}e - \frac{421}{37}$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $\phantom{-}\frac{25}{592}e^{5} + \frac{17}{296}e^{4} - \frac{863}{592}e^{3} - \frac{183}{74}e^{2} + \frac{220}{37}e + \frac{243}{37}$ |
| 41 | $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ | $\phantom{-}\frac{3}{296}e^{5} + \frac{5}{148}e^{4} - \frac{145}{296}e^{3} - \frac{75}{74}e^{2} + \frac{335}{74}e + \frac{8}{37}$ |
| 59 | $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ | $\phantom{-}\frac{61}{592}e^{5} + \frac{151}{296}e^{4} - \frac{1715}{592}e^{3} - \frac{2561}{148}e^{2} - \frac{329}{37}e + \frac{883}{37}$ |
| 61 | $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ | $-\frac{9}{148}e^{5} - \frac{15}{74}e^{4} + \frac{287}{148}e^{3} + \frac{262}{37}e^{2} - \frac{117}{37}e - \frac{344}{37}$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ | $-\frac{35}{296}e^{5} - \frac{83}{148}e^{4} + \frac{1001}{296}e^{3} + \frac{1393}{74}e^{2} + \frac{272}{37}e - \frac{784}{37}$ |
| 61 | $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ | $-\frac{57}{296}e^{5} - \frac{33}{37}e^{4} + \frac{1719}{296}e^{3} + \frac{4367}{148}e^{2} + \frac{203}{37}e - \frac{1373}{37}$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ | $-\frac{103}{296}e^{5} - \frac{221}{148}e^{4} + \frac{3153}{296}e^{3} + \frac{1861}{37}e^{2} + \frac{289}{74}e - \frac{2766}{37}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{219}{592}e^{5} + \frac{439}{296}e^{4} - \frac{6589}{592}e^{3} - \frac{1859}{37}e^{2} - \frac{278}{37}e + \frac{2327}{37}$ |
| 79 | $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ | $-\frac{65}{296}e^{5} - \frac{133}{148}e^{4} + \frac{2007}{296}e^{3} + \frac{1127}{37}e^{2} - \frac{71}{37}e - \frac{1715}{37}$ |
| 89 | $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ | $-\frac{77}{296}e^{5} - \frac{153}{148}e^{4} + \frac{2291}{296}e^{3} + \frac{2591}{74}e^{2} + \frac{405}{74}e - \frac{1636}{37}$ |
| 101 | $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ | $\phantom{-}\frac{11}{296}e^{5} + \frac{43}{148}e^{4} - \frac{285}{296}e^{3} - \frac{341}{37}e^{2} - \frac{243}{37}e + \frac{535}{37}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $-1$ |