Base field 4.4.9301.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - x^{10} - 25x^{9} + 17x^{8} + 232x^{7} - 69x^{6} - 992x^{5} - 104x^{4} + 1856x^{3} + 848x^{2} - 960x - 576\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}\frac{17}{216}e^{10} - \frac{41}{216}e^{9} - \frac{383}{216}e^{8} + \frac{817}{216}e^{7} + \frac{785}{54}e^{6} - \frac{589}{24}e^{5} - \frac{5975}{108}e^{4} + \frac{6295}{108}e^{3} + \frac{10391}{108}e^{2} - \frac{895}{27}e - \frac{433}{9}$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-\frac{13}{432}e^{10} + \frac{13}{108}e^{9} + \frac{19}{27}e^{8} - \frac{553}{216}e^{7} - \frac{2695}{432}e^{6} + \frac{863}{48}e^{5} + \frac{11681}{432}e^{4} - \frac{9893}{216}e^{3} - \frac{5921}{108}e^{2} + \frac{1361}{54}e + \frac{250}{9}$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}\frac{17}{864}e^{10} - \frac{95}{864}e^{9} - \frac{383}{864}e^{8} + \frac{2059}{864}e^{7} + \frac{1651}{432}e^{6} - \frac{1657}{96}e^{5} - \frac{7217}{432}e^{4} + \frac{10127}{216}e^{3} + \frac{3833}{108}e^{2} - \frac{865}{27}e - \frac{169}{9}$ |
| 16 | $[16, 2, 2]$ | $-\frac{133}{864}e^{10} + \frac{235}{864}e^{9} + \frac{2971}{864}e^{8} - \frac{4559}{864}e^{7} - \frac{11843}{432}e^{6} + \frac{3173}{96}e^{5} + \frac{42289}{432}e^{4} - \frac{16411}{216}e^{3} - \frac{8297}{54}e^{2} + \frac{2533}{54}e + \frac{671}{9}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{5}{432}e^{10} + \frac{17}{216}e^{9} - \frac{23}{108}e^{8} - \frac{373}{216}e^{7} + \frac{239}{432}e^{6} + \frac{599}{48}e^{5} + \frac{3221}{432}e^{4} - \frac{871}{27}e^{3} - \frac{992}{27}e^{2} + \frac{406}{27}e + \frac{241}{9}$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{7}{432}e^{10} - \frac{7}{108}e^{9} - \frac{113}{216}e^{8} + \frac{38}{27}e^{7} + \frac{2743}{432}e^{6} - \frac{479}{48}e^{5} - \frac{14963}{432}e^{4} + \frac{676}{27}e^{3} + \frac{8393}{108}e^{2} - \frac{328}{27}e - \frac{379}{9}$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ | $-1$ |
| 37 | $[37, 37, -w^{3} + 4w + 1]$ | $-\frac{7}{108}e^{10} + \frac{139}{432}e^{9} + \frac{607}{432}e^{8} - \frac{2837}{432}e^{7} - \frac{5059}{432}e^{6} + \frac{1051}{24}e^{5} + \frac{22133}{432}e^{4} - \frac{23117}{216}e^{3} - \frac{6067}{54}e^{2} + \frac{1690}{27}e + \frac{562}{9}$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 2w + 1]$ | $\phantom{-}\frac{23}{144}e^{10} - \frac{29}{144}e^{9} - \frac{533}{144}e^{8} + \frac{577}{144}e^{7} + \frac{2203}{72}e^{6} - \frac{415}{16}e^{5} - \frac{7997}{72}e^{4} + \frac{2177}{36}e^{3} + \frac{3047}{18}e^{2} - \frac{278}{9}e - \frac{212}{3}$ |
| 49 | $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ | $-\frac{11}{216}e^{10} + \frac{11}{54}e^{9} + \frac{28}{27}e^{8} - \frac{443}{108}e^{7} - \frac{1649}{216}e^{6} + \frac{649}{24}e^{5} + \frac{6079}{216}e^{4} - \frac{7075}{108}e^{3} - \frac{2983}{54}e^{2} + \frac{1000}{27}e + \frac{286}{9}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ | $-\frac{127}{432}e^{10} + \frac{265}{432}e^{9} + \frac{2893}{432}e^{8} - \frac{5249}{432}e^{7} - \frac{11867}{216}e^{6} + \frac{3755}{48}e^{5} + \frac{43795}{216}e^{4} - \frac{10007}{54}e^{3} - \frac{17533}{54}e^{2} + \frac{3058}{27}e + \frac{1390}{9}$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}\frac{37}{216}e^{10} - \frac{47}{108}e^{9} - \frac{104}{27}e^{8} + \frac{955}{108}e^{7} + \frac{6823}{216}e^{6} - \frac{1409}{24}e^{5} - \frac{26255}{216}e^{4} + \frac{7693}{54}e^{3} + \frac{11855}{54}e^{2} - \frac{2237}{27}e - \frac{1034}{9}$ |
| 67 | $[67, 67, w^{2} - 3w - 2]$ | $\phantom{-}\frac{11}{216}e^{10} - \frac{11}{54}e^{9} - \frac{28}{27}e^{8} + \frac{443}{108}e^{7} + \frac{1649}{216}e^{6} - \frac{649}{24}e^{5} - \frac{6079}{216}e^{4} + \frac{7075}{108}e^{3} + \frac{2821}{54}e^{2} - \frac{919}{27}e - \frac{160}{9}$ |
| 71 | $[71, 71, -w^{2} + 5]$ | $\phantom{-}\frac{1}{12}e^{10} - \frac{19}{48}e^{9} - \frac{85}{48}e^{8} + \frac{395}{48}e^{7} + \frac{673}{48}e^{6} - \frac{225}{4}e^{5} - \frac{2741}{48}e^{4} + \frac{424}{3}e^{3} + \frac{733}{6}e^{2} - \frac{262}{3}e - 73$ |
| 71 | $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ | $-\frac{197}{864}e^{10} + \frac{383}{864}e^{9} + \frac{4127}{864}e^{8} - \frac{7171}{864}e^{7} - \frac{14809}{432}e^{6} + \frac{4693}{96}e^{5} + \frac{44819}{432}e^{4} - \frac{21917}{216}e^{3} - \frac{13733}{108}e^{2} + \frac{1387}{27}e + \frac{367}{9}$ |
| 71 | $[71, 71, w^{2} - 2w - 5]$ | $-\frac{13}{144}e^{10} + \frac{17}{72}e^{9} + \frac{67}{36}e^{8} - \frac{337}{72}e^{7} - \frac{1939}{144}e^{6} + \frac{489}{16}e^{5} + \frac{6443}{144}e^{4} - \frac{2737}{36}e^{3} - \frac{2555}{36}e^{2} + \frac{460}{9}e + \frac{97}{3}$ |
| 79 | $[79, 79, w^{2} - 3w - 1]$ | $\phantom{-}\frac{23}{216}e^{10} - \frac{19}{108}e^{9} - \frac{271}{108}e^{8} + \frac{187}{54}e^{7} + \frac{4631}{216}e^{6} - \frac{529}{24}e^{5} - \frac{17821}{216}e^{4} + \frac{5515}{108}e^{3} + \frac{3731}{27}e^{2} - \frac{844}{27}e - \frac{616}{9}$ |
| 79 | $[79, 79, w^{3} - 6w - 1]$ | $-\frac{5}{144}e^{10} - \frac{7}{144}e^{9} + \frac{137}{144}e^{8} + \frac{143}{144}e^{7} - \frac{323}{36}e^{6} - \frac{103}{16}e^{5} + \frac{1213}{36}e^{4} + \frac{239}{18}e^{3} - \frac{815}{18}e^{2} + \frac{8}{9}e + \frac{80}{3}$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ | $-\frac{77}{432}e^{10} + \frac{23}{108}e^{9} + \frac{473}{108}e^{8} - \frac{941}{216}e^{7} - \frac{16943}{432}e^{6} + \frac{1399}{48}e^{5} + \frac{67933}{432}e^{4} - \frac{14911}{216}e^{3} - \frac{7198}{27}e^{2} + \frac{773}{27}e + \frac{1100}{9}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ | $1$ |