Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, -w^{3} + 5w + 1]$ |
| 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:
| \(x^{11} - 5x^{10} - 4x^{9} + 48x^{8} - 19x^{7} - 152x^{6} + 90x^{5} + 203x^{4} - 100x^{3} - 107x^{2} + 27x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}\frac{2}{9}e^{10} - \frac{8}{9}e^{9} - \frac{13}{9}e^{8} + \frac{71}{9}e^{7} + 2e^{6} - \frac{193}{9}e^{5} - \frac{22}{9}e^{4} + 22e^{3} + \frac{55}{9}e^{2} - \frac{20}{3}e - 2$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $-1$ |
| 11 | $[11, 11, -w + 2]$ | $-\frac{5}{9}e^{10} + \frac{23}{9}e^{9} + \frac{16}{9}e^{8} - \frac{188}{9}e^{7} + \frac{37}{3}e^{6} + \frac{424}{9}e^{5} - \frac{401}{9}e^{4} - \frac{98}{3}e^{3} + \frac{317}{9}e^{2} + \frac{16}{3}e - 3$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}\frac{2}{9}e^{10} + \frac{1}{9}e^{9} - \frac{40}{9}e^{8} - \frac{1}{9}e^{7} + 26e^{6} - \frac{22}{9}e^{5} - \frac{472}{9}e^{4} + 2e^{3} + \frac{289}{9}e^{2} + \frac{10}{3}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{1}{3}e^{10} + e^{9} + 4e^{8} - \frac{35}{3}e^{7} - \frac{52}{3}e^{6} + \frac{134}{3}e^{5} + \frac{100}{3}e^{4} - \frac{181}{3}e^{3} - \frac{77}{3}e^{2} + \frac{58}{3}e + 4$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-\frac{2}{9}e^{10} - \frac{1}{9}e^{9} + \frac{49}{9}e^{8} - \frac{26}{9}e^{7} - 34e^{6} + \frac{238}{9}e^{5} + \frac{643}{9}e^{4} - 53e^{3} - \frac{442}{9}e^{2} + \frac{77}{3}e + 3$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $\phantom{-}e^{10} - \frac{14}{3}e^{9} - \frac{10}{3}e^{8} + \frac{118}{3}e^{7} - \frac{65}{3}e^{6} - 96e^{5} + \frac{244}{3}e^{4} + \frac{247}{3}e^{3} - 66e^{2} - \frac{67}{3}e + 7$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $-\frac{8}{9}e^{10} + \frac{26}{9}e^{9} + \frac{58}{9}e^{8} - \frac{209}{9}e^{7} - \frac{32}{3}e^{6} + \frac{430}{9}e^{5} + \frac{19}{9}e^{4} - \frac{56}{3}e^{3} - \frac{40}{9}e^{2} - \frac{23}{3}e + 8$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e^{10} - \frac{13}{3}e^{9} - \frac{14}{3}e^{8} + \frac{110}{3}e^{7} - \frac{25}{3}e^{6} - 91e^{5} + \frac{125}{3}e^{4} + \frac{248}{3}e^{3} - 33e^{2} - \frac{80}{3}e + 6$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $-\frac{13}{9}e^{10} + \frac{52}{9}e^{9} + \frac{71}{9}e^{8} - \frac{439}{9}e^{7} + 4e^{6} + \frac{1079}{9}e^{5} - \frac{433}{9}e^{4} - 107e^{3} + \frac{385}{9}e^{2} + \frac{100}{3}e - 2$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $-\frac{7}{9}e^{10} + \frac{10}{9}e^{9} + \frac{104}{9}e^{8} - \frac{127}{9}e^{7} - 57e^{6} + \frac{536}{9}e^{5} + \frac{923}{9}e^{4} - 98e^{3} - \frac{467}{9}e^{2} + \frac{154}{3}e - 1$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $\phantom{-}\frac{1}{9}e^{10} - \frac{4}{9}e^{9} - \frac{11}{9}e^{8} + \frac{49}{9}e^{7} + 5e^{6} - \frac{200}{9}e^{5} - \frac{83}{9}e^{4} + 29e^{3} + \frac{32}{9}e^{2} + \frac{2}{3}e + 5$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $-\frac{1}{9}e^{10} + \frac{13}{9}e^{9} - \frac{25}{9}e^{8} - \frac{112}{9}e^{7} + 33e^{6} + \frac{290}{9}e^{5} - \frac{916}{9}e^{4} - 32e^{3} + \frac{913}{9}e^{2} + \frac{37}{3}e - 16$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $\phantom{-}\frac{2}{3}e^{10} - 3e^{9} - 3e^{8} + \frac{82}{3}e^{7} - \frac{31}{3}e^{6} - \frac{229}{3}e^{5} + \frac{166}{3}e^{4} + \frac{227}{3}e^{3} - \frac{170}{3}e^{2} - \frac{59}{3}e + 12$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $-\frac{1}{9}e^{10} + \frac{7}{9}e^{9} - \frac{1}{9}e^{8} - \frac{64}{9}e^{7} + \frac{16}{3}e^{6} + \frac{191}{9}e^{5} - \frac{85}{9}e^{4} - \frac{80}{3}e^{3} - \frac{23}{9}e^{2} + 10e + 4$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $\phantom{-}\frac{1}{9}e^{10} - \frac{16}{9}e^{9} + \frac{46}{9}e^{8} + \frac{82}{9}e^{7} - \frac{136}{3}e^{6} + \frac{70}{9}e^{5} + \frac{868}{9}e^{4} - \frac{163}{3}e^{3} - \frac{454}{9}e^{2} + 36e - 7$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $\phantom{-}\frac{1}{9}e^{10} + \frac{26}{9}e^{9} - \frac{131}{9}e^{8} - \frac{119}{9}e^{7} + \frac{352}{3}e^{6} - \frac{227}{9}e^{5} - \frac{2501}{9}e^{4} + \frac{337}{3}e^{3} + \frac{1832}{9}e^{2} - \frac{182}{3}e - 13$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $-\frac{11}{9}e^{10} + \frac{65}{9}e^{9} - \frac{26}{9}e^{8} - \frac{473}{9}e^{7} + \frac{247}{3}e^{6} + \frac{733}{9}e^{5} - \frac{2000}{9}e^{4} + \frac{64}{3}e^{3} + \frac{1484}{9}e^{2} - \frac{164}{3}e - 16$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $-\frac{19}{9}e^{10} + \frac{82}{9}e^{9} + \frac{104}{9}e^{8} - \frac{736}{9}e^{7} + \frac{17}{3}e^{6} + \frac{2000}{9}e^{5} - \frac{595}{9}e^{4} - \frac{625}{3}e^{3} + \frac{445}{9}e^{2} + \frac{128}{3}e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{3} + 5w + 1]$ | $1$ |