Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[21, 21, w^{3} - w^{2} - 5w - 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + x^{6} - 18x^{5} - 21x^{4} + 61x^{3} + 32x^{2} - 51x + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $-1$ |
| 4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-\frac{20}{317}e^{6} - \frac{62}{317}e^{5} + \frac{420}{317}e^{4} + \frac{985}{317}e^{3} - \frac{1529}{317}e^{2} - \frac{1727}{317}e + \frac{595}{317}$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $\phantom{-}\frac{85}{317}e^{6} + \frac{105}{317}e^{5} - \frac{1468}{317}e^{4} - \frac{2205}{317}e^{3} + \frac{4200}{317}e^{2} + \frac{4249}{317}e - \frac{2608}{317}$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $-\frac{10}{317}e^{6} - \frac{31}{317}e^{5} + \frac{210}{317}e^{4} + \frac{334}{317}e^{3} - \frac{606}{317}e^{2} + \frac{880}{317}e - \frac{495}{317}$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{78}{317}e^{6} - \frac{115}{317}e^{5} + \frac{1321}{317}e^{4} + \frac{2415}{317}e^{3} - \frac{3649}{317}e^{2} - \frac{5499}{317}e + \frac{2479}{317}$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $-\frac{1}{317}e^{6} + \frac{92}{317}e^{5} + \frac{21}{317}e^{4} - \frac{1298}{317}e^{3} - \frac{1075}{317}e^{2} + \frac{1673}{317}e + \frac{1060}{317}$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $-\frac{58}{317}e^{6} - \frac{53}{317}e^{5} + \frac{901}{317}e^{4} + \frac{1113}{317}e^{3} - \frac{1486}{317}e^{2} - \frac{602}{317}e - \frac{969}{317}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{44}{317}e^{6} - \frac{73}{317}e^{5} + \frac{607}{317}e^{4} + \frac{1533}{317}e^{3} - \frac{67}{317}e^{2} - \frac{3102}{317}e - \frac{910}{317}$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}\frac{56}{317}e^{6} - \frac{80}{317}e^{5} - \frac{859}{317}e^{4} + \frac{729}{317}e^{3} + \frac{2506}{317}e^{2} - \frac{2075}{317}e - \frac{81}{317}$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $-\frac{8}{317}e^{6} + \frac{102}{317}e^{5} + \frac{168}{317}e^{4} - \frac{1508}{317}e^{3} - \frac{1943}{317}e^{2} + \frac{2923}{317}e + \frac{2140}{317}$ |
| 43 | $[43, 43, w^{2} - 3w - 2]$ | $-\frac{81}{317}e^{6} - \frac{156}{317}e^{5} + \frac{1384}{317}e^{4} + \frac{2959}{317}e^{3} - \frac{3387}{317}e^{2} - \frac{5552}{317}e + \frac{587}{317}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{29}{317}e^{6} + \frac{132}{317}e^{5} + \frac{609}{317}e^{4} - \frac{1821}{317}e^{3} - \frac{4230}{317}e^{2} + \frac{3503}{317}e + \frac{2210}{317}$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $\phantom{-}\frac{125}{317}e^{6} + \frac{229}{317}e^{5} - \frac{1991}{317}e^{4} - \frac{4492}{317}e^{3} + \frac{3137}{317}e^{2} + \frac{8020}{317}e - \frac{628}{317}$ |
| 83 | $[83, 83, -w - 3]$ | $\phantom{-}\frac{53}{317}e^{6} - \frac{121}{317}e^{5} - \frac{796}{317}e^{4} + \frac{1273}{317}e^{3} + \frac{2768}{317}e^{2} - \frac{2128}{317}e - \frac{1973}{317}$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{222}{317}e^{6} - \frac{181}{317}e^{5} + \frac{3711}{317}e^{4} + \frac{4435}{317}e^{3} - \frac{10093}{317}e^{2} - \frac{7726}{317}e + \frac{4544}{317}$ |
| 89 | $[89, 89, 2w - 1]$ | $-\frac{5}{317}e^{6} - \frac{174}{317}e^{5} + \frac{105}{317}e^{4} + \frac{2703}{317}e^{3} + \frac{1282}{317}e^{2} - \frac{5900}{317}e - \frac{2625}{317}$ |
| 101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $\phantom{-}\frac{210}{317}e^{6} + \frac{334}{317}e^{5} - \frac{3459}{317}e^{4} - \frac{6697}{317}e^{3} + \frac{7654}{317}e^{2} + \frac{11635}{317}e - \frac{4187}{317}$ |
| 101 | $[101, 101, 2w^{2} - 3w - 3]$ | $-\frac{31}{317}e^{6} - \frac{1}{317}e^{5} + \frac{334}{317}e^{4} + \frac{338}{317}e^{3} + \frac{911}{317}e^{2} + \frac{826}{317}e - \frac{3595}{317}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $1$ |
| $7$ | $[7, 7, w - 2]$ | $-1$ |