Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, 4w + 19]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 4x^{8} - 6x^{7} - 35x^{6} + x^{5} + 90x^{4} + 31x^{3} - 67x^{2} - 29x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $\phantom{-}\frac{13}{9}e^{8} + \frac{17}{3}e^{7} - \frac{28}{3}e^{6} - \frac{452}{9}e^{5} + 8e^{4} + 133e^{3} + \frac{223}{9}e^{2} - \frac{965}{9}e - \frac{70}{3}$ |
| 2 | $[2, 2, w + 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 6w - 35]$ | $-\frac{19}{9}e^{8} - \frac{23}{3}e^{7} + \frac{46}{3}e^{6} + \frac{608}{9}e^{5} - 25e^{4} - 175e^{3} - \frac{94}{9}e^{2} + \frac{1211}{9}e + \frac{73}{3}$ |
| 7 | $[7, 7, -6w - 29]$ | $\phantom{-}\frac{13}{9}e^{8} + \frac{17}{3}e^{7} - \frac{28}{3}e^{6} - \frac{452}{9}e^{5} + 8e^{4} + 132e^{3} + \frac{214}{9}e^{2} - \frac{929}{9}e - \frac{64}{3}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{7}{3}e^{8} + 9e^{7} - 16e^{6} - \frac{242}{3}e^{5} + 20e^{4} + 216e^{3} + \frac{82}{3}e^{2} - \frac{521}{3}e - 36$ |
| 11 | $[11, 11, 4w + 19]$ | $\phantom{-}1$ |
| 11 | $[11, 11, 4w - 23]$ | $-\frac{16}{9}e^{8} - \frac{20}{3}e^{7} + \frac{37}{3}e^{6} + \frac{539}{9}e^{5} - 15e^{4} - 161e^{3} - \frac{226}{9}e^{2} + \frac{1178}{9}e + \frac{91}{3}$ |
| 13 | $[13, 13, -2w + 11]$ | $\phantom{-}\frac{4}{9}e^{8} + \frac{5}{3}e^{7} - \frac{10}{3}e^{6} - \frac{146}{9}e^{5} + 5e^{4} + 49e^{3} + \frac{43}{9}e^{2} - \frac{407}{9}e - \frac{28}{3}$ |
| 13 | $[13, 13, 2w + 9]$ | $-\frac{16}{9}e^{8} - \frac{20}{3}e^{7} + \frac{37}{3}e^{6} + \frac{530}{9}e^{5} - 17e^{4} - 154e^{3} - \frac{136}{9}e^{2} + \frac{1070}{9}e + \frac{70}{3}$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{4}{3}e^{8} + 5e^{7} - 9e^{6} - \frac{128}{3}e^{5} + 11e^{4} + 103e^{3} + \frac{43}{3}e^{2} - \frac{206}{3}e - 20$ |
| 31 | $[31, 31, 2w - 13]$ | $\phantom{-}\frac{22}{3}e^{8} + 27e^{7} - 51e^{6} - \frac{710}{3}e^{5} + 69e^{4} + 611e^{3} + \frac{211}{3}e^{2} - \frac{1400}{3}e - 98$ |
| 31 | $[31, 31, -2w - 11]$ | $\phantom{-}\frac{1}{9}e^{8} + \frac{2}{3}e^{7} - \frac{4}{3}e^{6} - \frac{77}{9}e^{5} + 4e^{4} + 32e^{3} + \frac{4}{9}e^{2} - \frac{311}{9}e - \frac{16}{3}$ |
| 41 | $[41, 41, -8w - 39]$ | $-\frac{1}{3}e^{8} - 2e^{7} + e^{6} + \frac{59}{3}e^{5} + 8e^{4} - 61e^{3} - \frac{85}{3}e^{2} + \frac{170}{3}e + 16$ |
| 41 | $[41, 41, 8w - 47]$ | $-\frac{28}{9}e^{8} - \frac{38}{3}e^{7} + \frac{58}{3}e^{6} + \frac{1022}{9}e^{5} - 11e^{4} - 306e^{3} - \frac{598}{9}e^{2} + \frac{2264}{9}e + \frac{175}{3}$ |
| 53 | $[53, 53, -26w - 125]$ | $-\frac{37}{9}e^{8} - \frac{47}{3}e^{7} + \frac{82}{3}e^{6} + \frac{1247}{9}e^{5} - 27e^{4} - 364e^{3} - \frac{607}{9}e^{2} + \frac{2597}{9}e + \frac{202}{3}$ |
| 53 | $[53, 53, 26w - 151]$ | $-\frac{8}{9}e^{8} - \frac{10}{3}e^{7} + \frac{20}{3}e^{6} + \frac{283}{9}e^{5} - 11e^{4} - 90e^{3} - \frac{50}{9}e^{2} + \frac{679}{9}e + \frac{32}{3}$ |
| 61 | $[61, 61, -14w + 81]$ | $-\frac{13}{3}e^{8} - 18e^{7} + 26e^{6} + \frac{485}{3}e^{5} - 7e^{4} - 436e^{3} - \frac{325}{3}e^{2} + \frac{1064}{3}e + 78$ |
| 61 | $[61, 61, -14w - 67]$ | $-\frac{52}{9}e^{8} - \frac{65}{3}e^{7} + \frac{118}{3}e^{6} + \frac{1700}{9}e^{5} - 50e^{4} - 483e^{3} - \frac{496}{9}e^{2} + \frac{3293}{9}e + \frac{205}{3}$ |
| 83 | $[83, 83, 2w - 15]$ | $-\frac{61}{9}e^{8} - \frac{77}{3}e^{7} + \frac{139}{3}e^{6} + \frac{2042}{9}e^{5} - 56e^{4} - 591e^{3} - \frac{775}{9}e^{2} + \frac{4049}{9}e + \frac{298}{3}$ |
| 83 | $[83, 83, -2w - 13]$ | $-\frac{28}{3}e^{8} - 34e^{7} + 66e^{6} + \frac{899}{3}e^{5} - 95e^{4} - 781e^{3} - \frac{229}{3}e^{2} + \frac{1826}{3}e + 121$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, 4w + 19]$ | $-1$ |