Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{2} + 2w + 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 4x^{9} - 9x^{8} - 41x^{7} + 32x^{6} + 134x^{5} - 82x^{4} - 140x^{3} + 121x^{2} - 15x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}\frac{44}{219}e^{9} + \frac{87}{73}e^{8} - \frac{22}{73}e^{7} - \frac{2479}{219}e^{6} - \frac{1624}{219}e^{5} + \frac{7517}{219}e^{4} + \frac{4229}{219}e^{3} - \frac{2640}{73}e^{2} + \frac{536}{219}e + \frac{256}{219}$ |
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $-\frac{130}{219}e^{9} - \frac{194}{73}e^{8} + \frac{284}{73}e^{7} + \frac{5642}{219}e^{6} - \frac{1075}{219}e^{5} - \frac{17242}{219}e^{4} + \frac{1133}{219}e^{3} + \frac{5902}{73}e^{2} - \frac{5665}{219}e - \frac{1274}{219}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{115}{219}e^{9} - \frac{166}{73}e^{8} + \frac{240}{73}e^{7} + \frac{4553}{219}e^{6} - \frac{454}{219}e^{5} - \frac{12136}{219}e^{4} - \frac{1870}{219}e^{3} + \frac{3104}{73}e^{2} + \frac{809}{219}e - \frac{1127}{219}$ |
| 29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $-\frac{122}{219}e^{9} - \frac{145}{73}e^{8} + \frac{426}{73}e^{7} + \frac{4594}{219}e^{6} - \frac{5153}{219}e^{5} - \frac{15278}{219}e^{4} + \frac{10861}{219}e^{3} + \frac{5276}{73}e^{2} - \frac{10943}{219}e + \frac{206}{219}$ |
| 29 | $[29, 29, -w^{2} + 2w + 3]$ | $-1$ |
| 31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{153}{73}e^{9} + \frac{667}{73}e^{8} - \frac{1069}{73}e^{7} - \frac{6465}{73}e^{6} + \frac{1852}{73}e^{5} + \frac{19567}{73}e^{4} - \frac{2657}{73}e^{3} - \frac{19364}{73}e^{2} + \frac{7080}{73}e + \frac{857}{73}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{409}{219}e^{9} + \frac{598}{73}e^{8} - \frac{898}{73}e^{7} - \frac{17006}{219}e^{6} + \frac{3340}{219}e^{5} + \frac{49492}{219}e^{4} - \frac{1319}{219}e^{3} - \frac{15342}{73}e^{2} + \frac{10537}{219}e + \frac{2957}{219}$ |
| 32 | $[32, 2, 2]$ | $-\frac{110}{219}e^{9} - \frac{181}{73}e^{8} + \frac{201}{73}e^{7} + \frac{5431}{219}e^{6} + \frac{118}{219}e^{5} - \frac{17807}{219}e^{4} - \frac{827}{219}e^{3} + \frac{6892}{73}e^{2} - \frac{6596}{219}e - \frac{1297}{219}$ |
| 43 | $[43, 43, -w^{2} - w + 4]$ | $-\frac{20}{73}e^{9} - \frac{112}{73}e^{8} + \frac{103}{73}e^{7} + \frac{1233}{73}e^{6} + \frac{121}{73}e^{5} - \frac{4545}{73}e^{4} - \frac{303}{73}e^{3} + \frac{5790}{73}e^{2} - \frac{1843}{73}e - \frac{415}{73}$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $-\frac{3}{73}e^{9} + \frac{27}{73}e^{8} + \frac{187}{73}e^{7} - \frac{118}{73}e^{6} - \frac{1482}{73}e^{5} - \frac{189}{73}e^{4} + \frac{3798}{73}e^{3} + \frac{686}{73}e^{2} - \frac{3368}{73}e + \frac{175}{73}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $\phantom{-}\frac{41}{219}e^{9} + \frac{23}{73}e^{8} - \frac{203}{73}e^{7} - \frac{553}{219}e^{6} + \frac{3245}{219}e^{5} + \frac{101}{219}e^{4} - \frac{6646}{219}e^{3} + \frac{1409}{73}e^{2} + \frac{3227}{219}e - \frac{1175}{219}$ |
| 73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $-\frac{46}{73}e^{9} - \frac{243}{73}e^{8} + \frac{215}{73}e^{7} + \frac{2449}{73}e^{6} + \frac{344}{73}e^{5} - \frac{8154}{73}e^{4} - \frac{821}{73}e^{3} + \frac{9521}{73}e^{2} - \frac{3122}{73}e + \frac{104}{73}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{141}{73}e^{9} + \frac{629}{73}e^{8} - \frac{978}{73}e^{7} - \frac{6207}{73}e^{6} + \frac{1618}{73}e^{5} + \frac{19322}{73}e^{4} - \frac{2430}{73}e^{3} - \frac{19978}{73}e^{2} + \frac{7332}{73}e + \frac{754}{73}$ |
| 81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $-\frac{290}{219}e^{9} - \frac{444}{73}e^{8} + \frac{583}{73}e^{7} + \frac{12805}{219}e^{6} - \frac{764}{219}e^{5} - \frac{38345}{219}e^{4} - \frac{2897}{219}e^{3} + \frac{12582}{73}e^{2} - \frac{7853}{219}e - \frac{3499}{219}$ |
| 83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $-\frac{373}{219}e^{9} - \frac{560}{73}e^{8} + \frac{807}{73}e^{7} + \frac{16232}{219}e^{6} - \frac{3076}{219}e^{5} - \frac{49414}{219}e^{4} + \frac{4142}{219}e^{3} + \frac{16613}{73}e^{2} - \frac{19177}{219}e - \frac{458}{219}$ |
| 89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{16}{219}e^{9} - \frac{98}{73}e^{8} - \frac{211}{73}e^{7} + \frac{2753}{219}e^{6} + \frac{6185}{219}e^{5} - \frac{8746}{219}e^{4} - \frac{12667}{219}e^{3} + \frac{3442}{73}e^{2} - \frac{394}{219}e + \frac{1858}{219}$ |
| 97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-\frac{326}{219}e^{9} - \frac{555}{73}e^{8} + \frac{455}{73}e^{7} + \frac{15550}{219}e^{6} + \frac{4009}{219}e^{5} - \frac{44993}{219}e^{4} - \frac{14042}{219}e^{3} + \frac{14450}{73}e^{2} - \frac{2060}{219}e - \frac{3808}{219}$ |
| 101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $-\frac{200}{219}e^{9} - \frac{276}{73}e^{8} + \frac{465}{73}e^{7} + \frac{7585}{219}e^{6} - \frac{2075}{219}e^{5} - \frac{19973}{219}e^{4} + \frac{328}{219}e^{3} + \frac{4700}{73}e^{2} - \frac{2954}{219}e - \frac{646}{219}$ |
| 103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $-\frac{755}{219}e^{9} - \frac{1166}{73}e^{8} + \frac{1509}{73}e^{7} + \frac{33643}{219}e^{6} - \frac{2495}{219}e^{5} - \frac{101585}{219}e^{4} - \frac{2879}{219}e^{3} + \frac{34131}{73}e^{2} - \frac{28091}{219}e - \frac{5647}{219}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{2} + 2w + 3]$ | $1$ |