Base field 6.6.1922000.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 8x^{4} - x^{3} + 12x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[16, 2, -3w^{5} + 4w^{4} + 23w^{3} - 6w^{2} - 35w - 6]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 2x^{5} - 53x^{4} - 74x^{3} + 689x^{2} + 880x - 1345\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ | $\phantom{-}\frac{19}{3575}e^{5} - \frac{251}{7150}e^{4} - \frac{236}{715}e^{3} + \frac{5789}{3575}e^{2} + \frac{2157}{715}e - \frac{15013}{1430}$ |
| 11 | $[11, 11, -w^{5} + w^{4} + 8w^{3} + w^{2} - 12w - 5]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{19}{3575}e^{5} + \frac{251}{7150}e^{4} + \frac{236}{715}e^{3} - \frac{5789}{3575}e^{2} - \frac{2872}{715}e + \frac{13583}{1430}$ |
| 31 | $[31, 31, -4w^{5} + 6w^{4} + 28w^{3} - 8w^{2} - 39w - 11]$ | $-3$ |
| 41 | $[41, 41, -4w^{5} + 5w^{4} + 31w^{3} - 4w^{2} - 49w - 16]$ | $-\frac{51}{7150}e^{5} + \frac{277}{7150}e^{4} + \frac{327}{715}e^{3} - \frac{4853}{3575}e^{2} - \frac{6173}{1430}e + \frac{2221}{1430}$ |
| 41 | $[41, 41, w^{4} - 3w^{3} - 3w^{2} + 8w + 1]$ | $\phantom{-}\frac{87}{3575}e^{5} - \frac{123}{7150}e^{4} - \frac{848}{715}e^{3} + \frac{5622}{3575}e^{2} + \frac{7441}{715}e - \frac{16559}{1430}$ |
| 41 | $[41, 41, -w^{2} + w + 2]$ | $-\frac{123}{7150}e^{5} - \frac{7}{325}e^{4} + \frac{521}{715}e^{3} - \frac{769}{3575}e^{2} - \frac{8709}{1430}e + \frac{3594}{715}$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{26}e^{5} + \frac{5}{286}e^{4} - \frac{469}{286}e^{3} + \frac{31}{26}e^{2} + \frac{1719}{143}e - \frac{2174}{143}$ |
| 59 | $[59, 59, 4w^{5} - 5w^{4} - 31w^{3} + 4w^{2} + 49w + 14]$ | $-\frac{107}{7150}e^{5} - \frac{311}{7150}e^{4} + \frac{963}{1430}e^{3} + \frac{5783}{7150}e^{2} - \frac{5398}{715}e - \frac{1479}{715}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + 3w^{2} - 8w - 3]$ | $-\frac{62}{3575}e^{5} + \frac{324}{3575}e^{4} + \frac{1701}{1430}e^{3} - \frac{23669}{7150}e^{2} - \frac{20177}{1430}e + \frac{10739}{1430}$ |
| 71 | $[71, 71, 5w^{5} - 7w^{4} - 37w^{3} + 9w^{2} + 55w + 16]$ | $\phantom{-}\frac{62}{3575}e^{5} + \frac{1}{3575}e^{4} - \frac{1311}{1430}e^{3} + \frac{2219}{7150}e^{2} + \frac{11467}{1430}e + \frac{5771}{1430}$ |
| 71 | $[71, 71, -w^{5} + 11w^{3} + 4w^{2} - 19w - 7]$ | $-\frac{173}{7150}e^{5} - \frac{29}{7150}e^{4} + \frac{1427}{1430}e^{3} - \frac{10563}{7150}e^{2} - \frac{3917}{715}e + \frac{15474}{715}$ |
| 71 | $[71, 71, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $\phantom{-}\frac{1}{550}e^{5} - \frac{27}{550}e^{4} - \frac{29}{110}e^{3} + \frac{1231}{550}e^{2} + \frac{294}{55}e - \frac{678}{55}$ |
| 79 | $[79, 79, 3w^{5} - 6w^{4} - 17w^{3} + 11w^{2} + 21w + 7]$ | $\phantom{-}\frac{43}{7150}e^{5} + \frac{307}{3575}e^{4} - \frac{127}{1430}e^{3} - \frac{20767}{7150}e^{2} - \frac{48}{715}e + \frac{9547}{1430}$ |
| 79 | $[79, 79, -5w^{5} + 8w^{4} + 35w^{3} - 14w^{2} - 52w - 11]$ | $\phantom{-}\frac{17}{1430}e^{5} - \frac{57}{715}e^{4} - \frac{21}{26}e^{3} + \frac{4427}{1430}e^{2} + \frac{1460}{143}e - \frac{503}{26}$ |
| 79 | $[79, 79, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 2]$ | $-\frac{14}{715}e^{5} - \frac{17}{715}e^{4} + \frac{239}{286}e^{3} + \frac{237}{1430}e^{2} - \frac{2149}{286}e - \frac{2063}{286}$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 14w^{3} - 3w^{2} - 21w - 9]$ | $\phantom{-}\frac{128}{3575}e^{5} - \frac{237}{7150}e^{4} - \frac{2759}{1430}e^{3} + \frac{13461}{7150}e^{2} + \frac{2773}{130}e - \frac{3298}{715}$ |
| 101 | $[101, 101, -2w^{5} + 2w^{4} + 17w^{3} - 29w - 9]$ | $-\frac{237}{7150}e^{5} - \frac{513}{3575}e^{4} + \frac{1483}{1430}e^{3} + \frac{24503}{7150}e^{2} - \frac{2798}{715}e - \frac{12643}{1430}$ |
| 101 | $[101, 101, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 9w + 1]$ | $-\frac{1}{286}e^{5} - \frac{2}{143}e^{4} + \frac{19}{286}e^{3} + \frac{177}{286}e^{2} + \frac{190}{143}e - \frac{2525}{286}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ | $-1$ |