Base field 3.3.1772.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x + 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - x^{10} - 15x^{9} + 14x^{8} + 80x^{7} - 66x^{6} - 182x^{5} + 113x^{4} + 167x^{3} - 38x^{2} - 54x - 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w^{2} + 11]$ | $-\frac{11}{13}e^{10} - \frac{9}{13}e^{9} + \frac{151}{13}e^{8} + 9e^{7} - \frac{698}{13}e^{6} - \frac{497}{13}e^{5} + \frac{1226}{13}e^{4} + \frac{797}{13}e^{3} - \frac{564}{13}e^{2} - 28e - \frac{17}{13}$ |
| 3 | $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ | $-\frac{7}{13}e^{10} - \frac{14}{13}e^{9} + \frac{89}{13}e^{8} + 14e^{7} - \frac{365}{13}e^{6} - \frac{776}{13}e^{5} + \frac{519}{13}e^{4} + \frac{1234}{13}e^{3} - \frac{80}{13}e^{2} - 40e - \frac{90}{13}$ |
| 5 | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{5}{2}w - 1]$ | $\phantom{-}\frac{14}{13}e^{10} + \frac{2}{13}e^{9} - \frac{191}{13}e^{8} - e^{7} + \frac{873}{13}e^{6} - \frac{21}{13}e^{5} - \frac{1493}{13}e^{4} + \frac{132}{13}e^{3} + \frac{628}{13}e^{2} + e - \frac{2}{13}$ |
| 25 | $[25, 5, \frac{7}{2}w^{2} - \frac{31}{2}w + 9]$ | $-\frac{29}{13}e^{10} - \frac{32}{13}e^{9} + \frac{391}{13}e^{8} + 31e^{7} - \frac{1761}{13}e^{6} - \frac{1640}{13}e^{5} + \frac{2984}{13}e^{4} + \frac{2464}{13}e^{3} - \frac{1286}{13}e^{2} - 76e - \frac{20}{13}$ |
| 29 | $[29, 29, -\frac{5}{2}w^{2} + \frac{1}{2}w + 29]$ | $-\frac{71}{13}e^{10} - \frac{25}{13}e^{9} + \frac{964}{13}e^{8} + 23e^{7} - \frac{4380}{13}e^{6} - \frac{1096}{13}e^{5} + \frac{7450}{13}e^{4} + \frac{1483}{13}e^{3} - \frac{3196}{13}e^{2} - 55e + \frac{77}{13}$ |
| 41 | $[41, 41, -w^{2} + 3w - 1]$ | $-\frac{47}{13}e^{10} - \frac{29}{13}e^{9} + \frac{631}{13}e^{8} + 28e^{7} - \frac{2837}{13}e^{6} - \frac{1470}{13}e^{5} + \frac{4833}{13}e^{4} + \frac{2272}{13}e^{3} - \frac{2190}{13}e^{2} - 85e - \frac{36}{13}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - \frac{3}{2}w + 3]$ | $\phantom{-}\frac{7}{13}e^{10} - \frac{25}{13}e^{9} - \frac{102}{13}e^{8} + 26e^{7} + \frac{508}{13}e^{6} - \frac{1525}{13}e^{5} - \frac{974}{13}e^{4} + \frac{2536}{13}e^{3} + \frac{587}{13}e^{2} - 74e - \frac{170}{13}$ |
| 41 | $[41, 41, 2w + 7]$ | $-2e^{10} + 27e^{8} - e^{7} - 121e^{6} + 10e^{5} + 197e^{4} - 20e^{3} - 65e^{2} - e - 6$ |
| 43 | $[43, 43, -\frac{7}{2}w^{2} - \frac{1}{2}w + 37]$ | $-\frac{72}{13}e^{10} - \frac{40}{13}e^{9} + \frac{973}{13}e^{8} + 39e^{7} - \frac{4369}{13}e^{6} - \frac{2089}{13}e^{5} + \frac{7188}{13}e^{4} + \frac{3366}{13}e^{3} - \frac{2537}{13}e^{2} - 138e - \frac{337}{13}$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{9}{2}w + 3]$ | $-\frac{68}{13}e^{10} - \frac{45}{13}e^{9} + \frac{911}{13}e^{8} + 44e^{7} - \frac{4049}{13}e^{6} - \frac{2355}{13}e^{5} + \frac{6598}{13}e^{4} + \frac{3686}{13}e^{3} - \frac{2339}{13}e^{2} - 130e - \frac{241}{13}$ |
| 43 | $[43, 43, \frac{1}{2}w^{2} - \frac{1}{2}w + 1]$ | $-\frac{2}{13}e^{10} - \frac{4}{13}e^{9} + \frac{31}{13}e^{8} + 4e^{7} - \frac{160}{13}e^{6} - \frac{218}{13}e^{5} + \frac{282}{13}e^{4} + \frac{295}{13}e^{3} - \frac{21}{13}e^{2} - e - \frac{22}{13}$ |
| 47 | $[47, 47, -w^{2} + w + 15]$ | $-\frac{43}{13}e^{10} - \frac{34}{13}e^{9} + \frac{582}{13}e^{8} + 32e^{7} - \frac{2647}{13}e^{6} - \frac{1619}{13}e^{5} + \frac{4607}{13}e^{4} + \frac{2319}{13}e^{3} - \frac{2252}{13}e^{2} - 71e + \frac{86}{13}$ |
| 53 | $[53, 53, -2w^{2} + 2w + 29]$ | $\phantom{-}\frac{38}{13}e^{10} + \frac{11}{13}e^{9} - \frac{511}{13}e^{8} - 9e^{7} + \frac{2299}{13}e^{6} + \frac{333}{13}e^{5} - \frac{3915}{13}e^{4} - \frac{262}{13}e^{3} + \frac{1855}{13}e^{2} + 8e - \frac{193}{13}$ |
| 59 | $[59, 59, w^{2} - w - 13]$ | $-3e^{10} - 2e^{9} + 40e^{8} + 25e^{7} - 176e^{6} - 100e^{5} + 280e^{4} + 150e^{3} - 89e^{2} - 70e - 7$ |
| 67 | $[67, 67, -\frac{1}{2}w^{2} + \frac{1}{2}w + 9]$ | $\phantom{-}\frac{68}{13}e^{10} + \frac{45}{13}e^{9} - \frac{924}{13}e^{8} - 43e^{7} + \frac{4205}{13}e^{6} + \frac{2225}{13}e^{5} - \frac{7196}{13}e^{4} - \frac{3348}{13}e^{3} + \frac{3132}{13}e^{2} + 122e + \frac{46}{13}$ |
| 71 | $[71, 71, 2w - 3]$ | $-\frac{27}{13}e^{10} - \frac{67}{13}e^{9} + \frac{347}{13}e^{8} + 67e^{7} - \frac{1458}{13}e^{6} - \frac{3723}{13}e^{5} + \frac{2247}{13}e^{4} + \frac{5913}{13}e^{3} - \frac{745}{13}e^{2} - 180e - \frac{258}{13}$ |
| 73 | $[73, 73, \frac{3}{2}w^{2} - \frac{11}{2}w + 1]$ | $\phantom{-}\frac{33}{13}e^{10} + \frac{53}{13}e^{9} - \frac{440}{13}e^{8} - 55e^{7} + \frac{1938}{13}e^{6} + \frac{3194}{13}e^{5} - \frac{3093}{13}e^{4} - \frac{5303}{13}e^{3} + \frac{912}{13}e^{2} + 166e + \frac{389}{13}$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} + \frac{15}{2}w - 5]$ | $\phantom{-}\frac{69}{13}e^{10} + \frac{47}{13}e^{9} - \frac{920}{13}e^{8} - 44e^{7} + \frac{4064}{13}e^{6} + \frac{2191}{13}e^{5} - \frac{6570}{13}e^{4} - \frac{3073}{13}e^{3} + \frac{2265}{13}e^{2} + 99e + \frac{252}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ | $-1$ |