Base field 4.4.10889.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, w^{3} - w^{2} - 5w + 4]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 20x^{10} + 150x^{8} - 532x^{6} + 912x^{4} - 671x^{2} + 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{1}{36}e^{11} - \frac{1}{3}e^{9} + \frac{1}{2}e^{7} + \frac{47}{9}e^{5} - \frac{143}{9}e^{3} + \frac{33}{4}e$ |
| 8 | $[8, 2, -w^{3} + 5w + 3]$ | $\phantom{-}\frac{5}{36}e^{11} - \frac{7}{3}e^{9} + \frac{27}{2}e^{7} - \frac{296}{9}e^{5} + \frac{308}{9}e^{3} - \frac{185}{12}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 5w + 4]$ | $-1$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 1]$ | $-\frac{1}{6}e^{11} + 3e^{9} - 19e^{7} + \frac{152}{3}e^{5} - \frac{152}{3}e^{3} + \frac{19}{2}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $\phantom{-}\frac{2}{9}e^{10} - \frac{11}{3}e^{8} + 20e^{6} - \frac{362}{9}e^{4} + \frac{179}{9}e^{2} + 4$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{6}e^{11} - \frac{8}{3}e^{9} + 14e^{7} - \frac{80}{3}e^{5} + \frac{25}{3}e^{3} + \frac{77}{6}e$ |
| 25 | $[25, 5, -w^{2} + 2]$ | $-2e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $-\frac{2}{9}e^{11} + 4e^{9} - 26e^{7} + \frac{686}{9}e^{5} - \frac{884}{9}e^{3} + \frac{112}{3}e$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $-\frac{7}{36}e^{11} + 3e^{9} - \frac{29}{2}e^{7} + \frac{193}{9}e^{5} + \frac{68}{9}e^{3} - \frac{253}{12}e$ |
| 37 | $[37, 37, 4w^{3} - 2w^{2} - 21w - 4]$ | $-\frac{4}{9}e^{10} + \frac{22}{3}e^{8} - 41e^{6} + \frac{823}{9}e^{4} - \frac{610}{9}e^{2} + 4$ |
| 43 | $[43, 43, 4w^{3} - 2w^{2} - 20w - 3]$ | $-\frac{11}{18}e^{11} + \frac{32}{3}e^{9} - 65e^{7} + \frac{1504}{9}e^{5} - \frac{1510}{9}e^{3} + \frac{251}{6}e$ |
| 47 | $[47, 47, -w^{3} + 6w]$ | $\phantom{-}\frac{1}{18}e^{11} - e^{9} + 7e^{7} - \frac{230}{9}e^{5} + \frac{428}{9}e^{3} - \frac{179}{6}e$ |
| 53 | $[53, 53, w^{3} - w^{2} - 5w - 2]$ | $-\frac{7}{9}e^{10} + \frac{40}{3}e^{8} - 79e^{6} + \frac{1753}{9}e^{4} - \frac{1684}{9}e^{2} + 55$ |
| 81 | $[81, 3, -3]$ | $-\frac{2}{3}e^{10} + 12e^{8} - 76e^{6} + \frac{614}{3}e^{4} - \frac{656}{3}e^{2} + 62$ |
| 83 | $[83, 83, 2w^{3} - w^{2} - 10w - 4]$ | $-\frac{10}{9}e^{10} + \frac{58}{3}e^{8} - 117e^{6} + \frac{2665}{9}e^{4} - \frac{2596}{9}e^{2} + 72$ |
| 89 | $[89, 89, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{1}{9}e^{10} + \frac{4}{3}e^{8} - 4e^{6} + \frac{28}{9}e^{4} - \frac{94}{9}e^{2} + 13$ |
| 89 | $[89, 89, 2w - 3]$ | $\phantom{-}\frac{2}{9}e^{11} - 4e^{9} + 26e^{7} - \frac{686}{9}e^{5} + \frac{884}{9}e^{3} - \frac{112}{3}e$ |
| 101 | $[101, 101, 6w^{3} - 3w^{2} - 31w - 5]$ | $-\frac{2}{9}e^{10} + \frac{14}{3}e^{8} - 35e^{6} + \frac{1001}{9}e^{4} - \frac{1232}{9}e^{2} + 48$ |
| 107 | $[107, 107, -w^{3} + w^{2} + 4w - 5]$ | $-\frac{7}{9}e^{10} + \frac{40}{3}e^{8} - 80e^{6} + \frac{1852}{9}e^{4} - \frac{1954}{9}e^{2} + 65$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^{3} - w^{2} - 5w + 4]$ | $1$ |