Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, w^{2} - 3w - 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 3x^{9} - 14x^{8} - 43x^{7} + 54x^{6} + 175x^{5} - 54x^{4} - 184x^{3} + 52x^{2} + 48x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{5}{24}e^{9} + \frac{5}{8}e^{8} - \frac{11}{4}e^{7} - \frac{211}{24}e^{6} + \frac{103}{12}e^{5} + \frac{823}{24}e^{4} + \frac{17}{12}e^{3} - \frac{185}{6}e^{2} - \frac{37}{6}e + 6$ |
| 7 | $[7, 7, w - 3]$ | $\phantom{-}\frac{13}{24}e^{9} + \frac{15}{8}e^{8} - \frac{20}{3}e^{7} - \frac{631}{24}e^{6} + \frac{33}{2}e^{5} + \frac{2435}{24}e^{4} + \frac{115}{6}e^{3} - \frac{262}{3}e^{2} - \frac{25}{2}e + \frac{49}{3}$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{7}{24}e^{9} + \frac{9}{8}e^{8} - \frac{19}{6}e^{7} - \frac{373}{24}e^{6} + 3e^{5} + \frac{1385}{24}e^{4} + \frac{95}{3}e^{3} - \frac{127}{3}e^{2} - \frac{35}{2}e + \frac{28}{3}$ |
| 9 | $[9, 3, w^{2} - 3w - 2]$ | $-1$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{3}e^{9} + \frac{5}{4}e^{8} - \frac{47}{12}e^{7} - \frac{35}{2}e^{6} + \frac{95}{12}e^{5} + \frac{403}{6}e^{4} + \frac{71}{4}e^{3} - \frac{113}{2}e^{2} - \frac{19}{3}e + \frac{31}{3}$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}\frac{3}{4}e^{9} + \frac{8}{3}e^{8} - \frac{37}{4}e^{7} - \frac{151}{4}e^{6} + \frac{275}{12}e^{5} + \frac{1781}{12}e^{4} + \frac{337}{12}e^{3} - \frac{817}{6}e^{2} - \frac{68}{3}e + \frac{89}{3}$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $-\frac{7}{24}e^{9} - \frac{9}{8}e^{8} + \frac{19}{6}e^{7} + \frac{373}{24}e^{6} - 3e^{5} - \frac{1385}{24}e^{4} - \frac{95}{3}e^{3} + \frac{124}{3}e^{2} + \frac{33}{2}e - \frac{25}{3}$ |
| 23 | $[23, 23, w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{6}e^{8} + \frac{1}{6}e^{7} - \frac{8}{3}e^{6} - \frac{13}{6}e^{5} + \frac{38}{3}e^{4} + \frac{15}{2}e^{3} - 17e^{2} - 4e + \frac{10}{3}$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{11}{24}e^{9} - \frac{11}{8}e^{8} + \frac{25}{4}e^{7} + \frac{469}{24}e^{6} - \frac{265}{12}e^{5} - \frac{1873}{24}e^{4} + \frac{145}{12}e^{3} + \frac{455}{6}e^{2} - \frac{41}{6}e - 14$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $-\frac{11}{8}e^{9} - \frac{113}{24}e^{8} + 17e^{7} + \frac{529}{8}e^{6} - \frac{257}{6}e^{5} - \frac{6143}{24}e^{4} - \frac{271}{6}e^{3} + \frac{667}{3}e^{2} + \frac{149}{6}e - \frac{133}{3}$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $-\frac{4}{3}e^{9} - \frac{59}{12}e^{8} + \frac{187}{12}e^{7} + \frac{413}{6}e^{6} - \frac{347}{12}e^{5} - \frac{1583}{6}e^{4} - \frac{1097}{12}e^{3} + \frac{1325}{6}e^{2} + \frac{176}{3}e - \frac{151}{3}$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-\frac{7}{12}e^{9} - \frac{25}{12}e^{8} + \frac{43}{6}e^{7} + \frac{119}{4}e^{6} - \frac{35}{2}e^{5} - \frac{479}{4}e^{4} - \frac{139}{6}e^{3} + \frac{361}{3}e^{2} + \frac{62}{3}e - \frac{86}{3}$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{3}e^{9} + \frac{5}{4}e^{8} - \frac{43}{12}e^{7} - \frac{101}{6}e^{6} + \frac{13}{4}e^{5} + \frac{349}{6}e^{4} + \frac{409}{12}e^{3} - \frac{157}{6}e^{2} - 10e - \frac{1}{3}$ |
| 41 | $[41, 41, w^{2} - w - 10]$ | $-\frac{23}{24}e^{9} - \frac{77}{24}e^{8} + \frac{49}{4}e^{7} + \frac{1081}{24}e^{6} - \frac{425}{12}e^{5} - \frac{1391}{8}e^{4} - \frac{139}{12}e^{3} + \frac{895}{6}e^{2} + \frac{17}{2}e - \frac{70}{3}$ |
| 43 | $[43, 43, -2w - 3]$ | $-e^{3} + 6e$ |
| 47 | $[47, 47, -w^{2} - w + 4]$ | $-\frac{23}{24}e^{9} - \frac{79}{24}e^{8} + 12e^{7} + \frac{1117}{24}e^{6} - \frac{63}{2}e^{5} - \frac{4385}{24}e^{4} - \frac{57}{2}e^{3} + 168e^{2} + \frac{137}{6}e - \frac{119}{3}$ |
| 49 | $[49, 7, -w^{2} + 5w - 5]$ | $\phantom{-}\frac{19}{24}e^{9} + \frac{23}{8}e^{8} - \frac{113}{12}e^{7} - \frac{973}{24}e^{6} + \frac{77}{4}e^{5} + \frac{3809}{24}e^{4} + \frac{581}{12}e^{3} - \frac{881}{6}e^{2} - \frac{73}{2}e + \frac{112}{3}$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}\frac{7}{24}e^{9} + \frac{23}{24}e^{8} - \frac{10}{3}e^{7} - \frac{103}{8}e^{6} + \frac{31}{6}e^{5} + \frac{1081}{24}e^{4} + \frac{151}{6}e^{3} - \frac{79}{3}e^{2} - \frac{43}{2}e + 9$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{19}{24}e^{9} - \frac{25}{8}e^{8} + 9e^{7} + \frac{1049}{24}e^{6} - \frac{85}{6}e^{5} - \frac{3989}{24}e^{4} - \frac{377}{6}e^{3} + \frac{395}{3}e^{2} + \frac{209}{6}e - 25$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w^{2} - 3w - 2]$ | $1$ |