Base field 6.6.1279733.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 10x^{8} + 15x^{7} - 115x^{6} - 281x^{5} + 515x^{4} + 1326x^{3} - 1268x^{2} - 2069x + 1697\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 6w - 1]$ | $-\frac{2089}{29705}e^{8} - \frac{17168}{29705}e^{7} - \frac{682}{2285}e^{6} + \frac{184023}{29705}e^{5} + \frac{36182}{5941}e^{4} - \frac{143937}{5941}e^{3} - \frac{393164}{29705}e^{2} + \frac{1055944}{29705}e - \frac{313211}{29705}$ |
| 7 | $[7, 7, -w^{4} + w^{3} + 4w^{2} - w - 1]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 3w - 3]$ | $\phantom{-}\frac{5223}{29705}e^{8} + \frac{45441}{29705}e^{7} + \frac{2974}{2285}e^{6} - \frac{472686}{29705}e^{5} - \frac{124682}{5941}e^{4} + \frac{371102}{5941}e^{3} + \frac{1421583}{29705}e^{2} - \frac{3062083}{29705}e + \frac{924802}{29705}$ |
| 29 | $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{4} - 5w^{2} - 2w + 4]$ | $\phantom{-}\frac{2064}{5941}e^{8} + \frac{15879}{5941}e^{7} - \frac{159}{457}e^{6} - \frac{200167}{5941}e^{5} - \frac{78203}{5941}e^{4} + \frac{952543}{5941}e^{3} + \frac{13462}{5941}e^{2} - \frac{1730441}{5941}e + \frac{965609}{5941}$ |
| 29 | $[29, 29, -w^{4} + w^{3} + 3w^{2} - w + 2]$ | $-\frac{4772}{29705}e^{8} - \frac{29079}{29705}e^{7} + \frac{6019}{2285}e^{6} + \frac{577614}{29705}e^{5} - \frac{92512}{5941}e^{4} - \frac{724662}{5941}e^{3} + \frac{2096053}{29705}e^{2} + \frac{7609607}{29705}e - \frac{5825553}{29705}$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $-\frac{4388}{29705}e^{8} - \frac{53481}{29705}e^{7} - \frac{13364}{2285}e^{6} + \frac{206296}{29705}e^{5} + \frac{355652}{5941}e^{4} + \frac{175570}{5941}e^{3} - \frac{5135508}{29705}e^{2} - \frac{3299612}{29705}e + \frac{4644598}{29705}$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 4w^{3} - w^{2} - 3w - 1]$ | $\phantom{-}\frac{12084}{29705}e^{8} + \frac{91688}{29705}e^{7} - \frac{2363}{2285}e^{6} - \frac{1234323}{29705}e^{5} - \frac{68352}{5941}e^{4} + \frac{1239701}{5941}e^{3} - \frac{281306}{29705}e^{2} - \frac{11757339}{29705}e + \frac{6974451}{29705}$ |
| 43 | $[43, 43, 2w^{3} - 2w^{2} - 7w + 3]$ | $\phantom{-}\frac{589}{5941}e^{8} + \frac{5179}{5941}e^{7} + \frac{492}{457}e^{6} - \frac{41696}{5941}e^{5} - \frac{72369}{5941}e^{4} + \frac{117892}{5941}e^{3} + \frac{151198}{5941}e^{2} - \frac{146699}{5941}e - \frac{14913}{5941}$ |
| 43 | $[43, 43, w^{3} - w^{2} - 2w + 1]$ | $-\frac{10887}{29705}e^{8} - \frac{86529}{29705}e^{7} - \frac{986}{2285}e^{6} + \frac{1033449}{29705}e^{5} + \frac{126596}{5941}e^{4} - \frac{941725}{5941}e^{3} - \frac{795482}{29705}e^{2} + \frac{8400552}{29705}e - \frac{4361588}{29705}$ |
| 64 | $[64, 2, -2]$ | $-\frac{7187}{29705}e^{8} - \frac{56164}{29705}e^{7} + \frac{549}{2285}e^{6} + \frac{737429}{29705}e^{5} + \frac{58157}{5941}e^{4} - \frac{753838}{5941}e^{3} - \frac{64762}{29705}e^{2} + \frac{7460807}{29705}e - \frac{4292068}{29705}$ |
| 71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $-\frac{277}{5941}e^{8} - \frac{499}{5941}e^{7} + \frac{1211}{457}e^{6} + \frac{51160}{5941}e^{5} - \frac{116508}{5941}e^{4} - \frac{414435}{5941}e^{3} + \frac{366046}{5941}e^{2} + \frac{923345}{5941}e - \frac{650622}{5941}$ |
| 71 | $[71, 71, w^{5} - 2w^{4} - 2w^{3} + 5w^{2} - 3w - 1]$ | $\phantom{-}\frac{24}{5941}e^{8} + \frac{2188}{5941}e^{7} + \frac{1502}{457}e^{6} + \frac{29519}{5941}e^{5} - \frac{170366}{5941}e^{4} - \frac{375158}{5941}e^{3} + \frac{547972}{5941}e^{2} + \frac{918902}{5941}e - \frac{864655}{5941}$ |
| 83 | $[83, 83, -2w^{4} + 3w^{3} + 6w^{2} - 7w + 2]$ | $-\frac{11003}{29705}e^{8} - \frac{107006}{29705}e^{7} - \frac{14339}{2285}e^{6} + \frac{844236}{29705}e^{5} + \frac{439016}{5941}e^{4} - \frac{428963}{5941}e^{3} - \frac{5759023}{29705}e^{2} + \frac{2388788}{29705}e + \frac{2076148}{29705}$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ | $-\frac{4152}{29705}e^{8} - \frac{51769}{29705}e^{7} - \frac{13066}{2285}e^{6} + \frac{216349}{29705}e^{5} + \frac{354087}{5941}e^{4} + \frac{143154}{5941}e^{3} - \frac{5125702}{29705}e^{2} - \frac{2822743}{29705}e + \frac{4280337}{29705}$ |
| 83 | $[83, 83, -w^{5} + 3w^{4} + w^{3} - 9w^{2} + 5w + 3]$ | $\phantom{-}\frac{928}{5941}e^{8} + \frac{9350}{5941}e^{7} + \frac{1257}{457}e^{6} - \frac{84425}{5941}e^{5} - \frac{216753}{5941}e^{4} + \frac{259256}{5941}e^{3} + \frac{604666}{5941}e^{2} - \frac{378507}{5941}e - \frac{141943}{5941}$ |
| 83 | $[83, 83, w^{5} - 7w^{3} + 10w - 1]$ | $-\frac{4902}{29705}e^{8} - \frac{60734}{29705}e^{7} - \frac{15446}{2285}e^{6} + \frac{237014}{29705}e^{5} + \frac{417816}{5941}e^{4} + \frac{209518}{5941}e^{3} - \frac{6090307}{29705}e^{2} - \frac{3897928}{29705}e + \frac{5494587}{29705}$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 1]$ | $-\frac{718}{2285}e^{8} - \frac{7571}{2285}e^{7} - \frac{17092}{2285}e^{6} + \frac{51036}{2285}e^{5} + \frac{38010}{457}e^{4} - \frac{14606}{457}e^{3} - \frac{510613}{2285}e^{2} - \frac{1097}{2285}e + \frac{256668}{2285}$ |
| 97 | $[97, 97, w^{5} - 5w^{3} - w^{2} + 3w - 3]$ | $-\frac{14043}{29705}e^{8} - \frac{77201}{29705}e^{7} + \frac{23146}{2285}e^{6} + \frac{1758946}{29705}e^{5} - \frac{405794}{5941}e^{4} - \frac{2317818}{5941}e^{3} + \frac{8015092}{29705}e^{2} + \frac{24261408}{29705}e - \frac{18221637}{29705}$ |
| 113 | $[113, 113, w^{4} - w^{3} - 4w^{2} + w + 4]$ | $\phantom{-}\frac{380}{5941}e^{8} + \frac{2958}{5941}e^{7} + \frac{170}{457}e^{6} - \frac{20768}{5941}e^{5} - \frac{20051}{5941}e^{4} + \frac{34664}{5941}e^{3} + \frac{18206}{5941}e^{2} + \frac{25517}{5941}e - \frac{56766}{5941}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 2]$ | $-1$ |