Base field 6.6.1541581.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 4x^{9} - 13x^{8} - 57x^{7} + 35x^{6} + 189x^{5} - 43x^{4} - 130x^{3} + 53x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ | $\phantom{-}\frac{5794}{5043}e^{9} + \frac{8386}{1681}e^{8} - \frac{66622}{5043}e^{7} - \frac{353363}{5043}e^{6} + \frac{79987}{5043}e^{5} + \frac{1128893}{5043}e^{4} + \frac{48392}{1681}e^{3} - \frac{736264}{5043}e^{2} + \frac{20577}{1681}e + \frac{27731}{5043}$ |
| 11 | $[11, 11, w^{2} - w - 2]$ | $\phantom{-}\frac{1711}{1681}e^{9} + \frac{7485}{1681}e^{8} - \frac{19487}{1681}e^{7} - \frac{105024}{1681}e^{6} + \frac{21008}{1681}e^{5} + \frac{333621}{1681}e^{4} + \frac{52254}{1681}e^{3} - \frac{208336}{1681}e^{2} + \frac{4570}{1681}e + \frac{5721}{1681}$ |
| 17 | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $-\frac{1759}{1681}e^{9} - \frac{7694}{1681}e^{8} + \frac{20072}{1681}e^{7} + \frac{107652}{1681}e^{6} - \frac{23018}{1681}e^{5} - \frac{338572}{1681}e^{4} - \frac{41052}{1681}e^{3} + \frac{201103}{1681}e^{2} - \frac{30373}{1681}e - \frac{3780}{1681}$ |
| 27 | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $-\frac{551}{5043}e^{9} - \frac{718}{1681}e^{8} + \frac{7871}{5043}e^{7} + \frac{33109}{5043}e^{6} - \frac{26225}{5043}e^{5} - \frac{133564}{5043}e^{4} + \frac{5531}{1681}e^{3} + \frac{153677}{5043}e^{2} + \frac{11058}{1681}e - \frac{24892}{5043}$ |
| 27 | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}1$ |
| 37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{18613}{5043}e^{9} + \frac{26396}{1681}e^{8} - \frac{221908}{5043}e^{7} - \frac{1116980}{5043}e^{6} + \frac{370306}{5043}e^{5} + \frac{3605231}{5043}e^{4} + \frac{30153}{1681}e^{3} - \frac{2368426}{5043}e^{2} + \frac{144784}{1681}e + \frac{56213}{5043}$ |
| 47 | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $-\frac{1079}{5043}e^{9} - \frac{2605}{1681}e^{8} - \frac{823}{5043}e^{7} + \frac{102361}{5043}e^{6} + \frac{168514}{5043}e^{5} - \frac{260308}{5043}e^{4} - \frac{195459}{1681}e^{3} + \frac{69071}{5043}e^{2} + \frac{89590}{1681}e - \frac{28756}{5043}$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $-\frac{2941}{5043}e^{9} - \frac{3930}{1681}e^{8} + \frac{38470}{5043}e^{7} + \frac{168164}{5043}e^{6} - \frac{107395}{5043}e^{5} - \frac{555677}{5043}e^{4} + \frac{50109}{1681}e^{3} + \frac{360241}{5043}e^{2} - \frac{62299}{1681}e + \frac{3463}{5043}$ |
| 59 | $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ | $-\frac{4154}{1681}e^{9} - \frac{17737}{1681}e^{8} + \frac{49156}{1681}e^{7} + \frac{250125}{1681}e^{6} - \frac{76871}{1681}e^{5} - \frac{807043}{1681}e^{4} - \frac{42102}{1681}e^{3} + \frac{530362}{1681}e^{2} - \frac{85347}{1681}e - \frac{9158}{1681}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{13327}{5043}e^{9} + \frac{18794}{1681}e^{8} - \frac{159376}{5043}e^{7} - \frac{794792}{5043}e^{6} + \frac{268726}{5043}e^{5} + \frac{2560535}{5043}e^{4} + \frac{26573}{1681}e^{3} - \frac{1660255}{5043}e^{2} + \frac{90420}{1681}e + \frac{18446}{5043}$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ | $-\frac{12299}{5043}e^{9} - \frac{17909}{1681}e^{8} + \frac{139703}{5043}e^{7} + \frac{751957}{5043}e^{6} - \frac{147512}{5043}e^{5} - \frac{2373673}{5043}e^{4} - \frac{120271}{1681}e^{3} + \frac{1460891}{5043}e^{2} - \frac{52042}{1681}e - \frac{35221}{5043}$ |
| 67 | $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ | $\phantom{-}\frac{2299}{5043}e^{9} + \frac{2648}{1681}e^{8} - \frac{36319}{5043}e^{7} - \frac{120407}{5043}e^{6} + \frac{167503}{5043}e^{5} + \frac{465293}{5043}e^{4} - \frac{114895}{1681}e^{3} - \frac{446266}{5043}e^{2} + \frac{72285}{1681}e - \frac{826}{5043}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-\frac{893}{5043}e^{9} - \frac{584}{1681}e^{8} + \frac{20234}{5043}e^{7} + \frac{34183}{5043}e^{6} - \frac{147710}{5043}e^{5} - \frac{200989}{5043}e^{4} + \frac{121649}{1681}e^{3} + \frac{320882}{5043}e^{2} - \frac{55057}{1681}e - \frac{40690}{5043}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}\frac{7783}{5043}e^{9} + \frac{11588}{1681}e^{8} - \frac{84244}{5043}e^{7} - \frac{481172}{5043}e^{6} + \frac{36571}{5043}e^{5} + \frac{1466744}{5043}e^{4} + \frac{131736}{1681}e^{3} - \frac{793654}{5043}e^{2} - \frac{1139}{1681}e + \frac{28304}{5043}$ |
| 73 | $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ | $-\frac{36775}{5043}e^{9} - \frac{52546}{1681}e^{8} + \frac{432541}{5043}e^{7} + \frac{2219774}{5043}e^{6} - \frac{645451}{5043}e^{5} - \frac{7133300}{5043}e^{4} - \frac{160879}{1681}e^{3} + \frac{4650055}{5043}e^{2} - \frac{204657}{1681}e - \frac{162077}{5043}$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $-\frac{18962}{5043}e^{9} - \frac{26564}{1681}e^{8} + \frac{228788}{5043}e^{7} + \frac{1123060}{5043}e^{6} - \frac{414548}{5043}e^{5} - \frac{3616189}{5043}e^{4} + \frac{8273}{1681}e^{3} + \frac{2347670}{5043}e^{2} - \frac{176327}{1681}e - \frac{26446}{5043}$ |
| 83 | $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ | $-\frac{2992}{5043}e^{9} - \frac{3969}{1681}e^{8} + \frac{38146}{5043}e^{7} + \frac{167174}{5043}e^{6} - \frac{95032}{5043}e^{5} - \frac{533306}{5043}e^{4} + \frac{34955}{1681}e^{3} + \frac{330808}{5043}e^{2} - \frac{46958}{1681}e - \frac{1724}{5043}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ | $\phantom{-}\frac{15304}{5043}e^{9} + \frac{20998}{1681}e^{8} - \frac{190720}{5043}e^{7} - \frac{891686}{5043}e^{6} + \frac{418963}{5043}e^{5} + \frac{2905133}{5043}e^{4} - \frac{91710}{1681}e^{3} - \frac{1932520}{5043}e^{2} + \frac{179601}{1681}e + \frac{5636}{5043}$ |
| 97 | $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ | $-\frac{24362}{5043}e^{9} - \frac{35242}{1681}e^{8} + \frac{281993}{5043}e^{7} + \frac{1489312}{5043}e^{6} - \frac{363308}{5043}e^{5} - \frac{4795987}{5043}e^{4} - \frac{175131}{1681}e^{3} + \frac{3200669}{5043}e^{2} - \frac{94155}{1681}e - \frac{163615}{5043}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-1$ |