Base field 4.4.15529.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^{3} + w^{2} + 5w + 1]$ |
| 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:
| \(x^{9} + 2x^{8} - 11x^{7} - 19x^{6} + 36x^{5} + 47x^{4} - 41x^{3} - 31x^{2} + 11x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{1}{10}e^{8} - \frac{3}{10}e^{7} + e^{6} + \frac{33}{10}e^{5} - \frac{27}{10}e^{4} - \frac{53}{5}e^{3} + \frac{21}{10}e^{2} + \frac{44}{5}e - \frac{11}{10}$ |
| 8 | $[8, 2, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}\frac{2}{5}e^{7} + \frac{4}{5}e^{6} - \frac{19}{5}e^{5} - \frac{32}{5}e^{4} + \frac{46}{5}e^{3} + \frac{51}{5}e^{2} - \frac{28}{5}e - \frac{13}{5}$ |
| 9 | $[9, 3, -w^{3} + w^{2} + 5w + 1]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}\frac{7}{10}e^{8} + \frac{3}{2}e^{7} - \frac{36}{5}e^{6} - \frac{139}{10}e^{5} + \frac{41}{2}e^{4} + \frac{162}{5}e^{3} - \frac{37}{2}e^{2} - \frac{96}{5}e + \frac{21}{10}$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $-\frac{2}{5}e^{8} - \frac{4}{5}e^{7} + \frac{19}{5}e^{6} + \frac{32}{5}e^{5} - \frac{46}{5}e^{4} - \frac{51}{5}e^{3} + \frac{33}{5}e^{2} + \frac{13}{5}e - 2$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-\frac{1}{5}e^{8} - \frac{4}{5}e^{7} + \frac{8}{5}e^{6} + 8e^{5} - \frac{11}{5}e^{4} - \frac{104}{5}e^{3} - \frac{7}{5}e^{2} + \frac{62}{5}e + \frac{13}{5}$ |
| 29 | $[29, 29, w^{2} - 3w - 1]$ | $-\frac{3}{10}e^{8} - \frac{9}{10}e^{7} + 3e^{6} + \frac{89}{10}e^{5} - \frac{81}{10}e^{4} - \frac{114}{5}e^{3} + \frac{63}{10}e^{2} + \frac{62}{5}e - \frac{33}{10}$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-\frac{1}{10}e^{8} + \frac{1}{10}e^{7} + \frac{9}{5}e^{6} - \frac{3}{2}e^{5} - \frac{101}{10}e^{4} + \frac{33}{5}e^{3} + \frac{183}{10}e^{2} - \frac{44}{5}e - \frac{67}{10}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $-\frac{2}{5}e^{8} - \frac{4}{5}e^{7} + \frac{19}{5}e^{6} + \frac{32}{5}e^{5} - \frac{41}{5}e^{4} - \frac{46}{5}e^{3} - \frac{7}{5}e^{2} - \frac{12}{5}e + 3$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{4}{5}e^{8} + \frac{7}{5}e^{7} - 9e^{6} - \frac{62}{5}e^{5} + \frac{148}{5}e^{4} + \frac{124}{5}e^{3} - \frac{149}{5}e^{2} - \frac{37}{5}e + \frac{14}{5}$ |
| 47 | $[47, 47, -w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{5}e^{8} - \frac{16}{5}e^{6} - \frac{2}{5}e^{5} + 16e^{4} + \frac{17}{5}e^{3} - 26e^{2} - \frac{21}{5}e + \frac{43}{5}$ |
| 47 | $[47, 47, 2w^{3} - 2w^{2} - 11w - 5]$ | $\phantom{-}\frac{3}{5}e^{8} + \frac{4}{5}e^{7} - 8e^{6} - \frac{39}{5}e^{5} + \frac{171}{5}e^{4} + \frac{98}{5}e^{3} - \frac{243}{5}e^{2} - \frac{49}{5}e + \frac{43}{5}$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 2w + 1]$ | $-\frac{6}{5}e^{8} - \frac{11}{5}e^{7} + \frac{64}{5}e^{6} + \frac{99}{5}e^{5} - \frac{194}{5}e^{4} - 45e^{3} + \frac{177}{5}e^{2} + 31e - \frac{9}{5}$ |
| 59 | $[59, 59, -w - 3]$ | $-\frac{4}{5}e^{8} - \frac{9}{5}e^{7} + \frac{46}{5}e^{6} + \frac{91}{5}e^{5} - \frac{166}{5}e^{4} - 50e^{3} + \frac{213}{5}e^{2} + 36e - \frac{41}{5}$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $\phantom{-}\frac{11}{10}e^{8} + \frac{17}{10}e^{7} - \frac{61}{5}e^{6} - \frac{151}{10}e^{5} + \frac{383}{10}e^{4} + \frac{164}{5}e^{3} - \frac{319}{10}e^{2} - \frac{87}{5}e - \frac{5}{2}$ |
| 73 | $[73, 73, 2w^{3} - 2w^{2} - 12w - 5]$ | $\phantom{-}\frac{13}{10}e^{8} + \frac{23}{10}e^{7} - \frac{76}{5}e^{6} - \frac{227}{10}e^{5} + \frac{537}{10}e^{4} + 61e^{3} - \frac{601}{10}e^{2} - 45e + \frac{47}{10}$ |
| 79 | $[79, 79, 4w^{3} - 4w^{2} - 22w - 7]$ | $-e^{8} - \frac{13}{5}e^{7} + \frac{49}{5}e^{6} + \frac{121}{5}e^{5} - \frac{132}{5}e^{4} - \frac{279}{5}e^{3} + \frac{116}{5}e^{2} + \frac{147}{5}e + \frac{12}{5}$ |
| 97 | $[97, 97, 2w^{3} - 3w^{2} - 9w + 1]$ | $-\frac{1}{10}e^{8} + \frac{1}{2}e^{7} + \frac{8}{5}e^{6} - \frac{73}{10}e^{5} - \frac{17}{2}e^{4} + \frac{149}{5}e^{3} + \frac{35}{2}e^{2} - \frac{147}{5}e - \frac{113}{10}$ |
| 101 | $[101, 101, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{9}{10}e^{8} + \frac{13}{10}e^{7} - \frac{54}{5}e^{6} - \frac{129}{10}e^{5} + \frac{387}{10}e^{4} + \frac{171}{5}e^{3} - \frac{421}{10}e^{2} - \frac{103}{5}e + \frac{9}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, -w^{3} + w^{2} + 5w + 1]$ | $-1$ |