Base field 6.6.703493.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[43,43,w^{5} - 7w^{3} - w^{2} + 10w + 3]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 2x^{7} - 43x^{6} + 48x^{5} + 451x^{4} - 196x^{3} - 1156x^{2} - 768x - 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ | $-\frac{1849}{18909}e^{7} + \frac{18233}{75636}e^{6} + \frac{77173}{18909}e^{5} - \frac{15175}{2292}e^{4} - \frac{69461}{1719}e^{3} + \frac{2957617}{75636}e^{2} + \frac{152975}{1719}e + \frac{176069}{6303}$ |
| 13 | $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ | $\phantom{-}\frac{5273}{37818}e^{7} - \frac{12799}{37818}e^{6} - \frac{220901}{37818}e^{5} + \frac{3511}{382}e^{4} + \frac{201343}{3438}e^{3} - \frac{2002487}{37818}e^{2} - \frac{233627}{1719}e - \frac{273224}{6303}$ |
| 13 | $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ | $\phantom{-}\frac{527}{75636}e^{7} - \frac{431}{37818}e^{6} - \frac{25391}{75636}e^{5} + \frac{152}{573}e^{4} + \frac{30835}{6876}e^{3} - \frac{32473}{37818}e^{2} - \frac{30820}{1719}e - \frac{36874}{6303}$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e$ |
| 41 | $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ | $\phantom{-}\frac{5273}{37818}e^{7} - \frac{12799}{37818}e^{6} - \frac{220901}{37818}e^{5} + \frac{3511}{382}e^{4} + \frac{201343}{3438}e^{3} - \frac{2002487}{37818}e^{2} - \frac{230189}{1719}e - \frac{273224}{6303}$ |
| 41 | $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ | $-\frac{31025}{151272}e^{7} + \frac{9749}{18909}e^{6} + \frac{1300823}{151272}e^{5} - \frac{10909}{764}e^{4} - \frac{1195633}{13752}e^{3} + \frac{6335203}{75636}e^{2} + \frac{352667}{1719}e + \frac{436805}{6303}$ |
| 41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $\phantom{-}\frac{12269}{75636}e^{7} - \frac{16349}{37818}e^{6} - \frac{506087}{75636}e^{5} + \frac{14011}{1146}e^{4} + \frac{447763}{6876}e^{3} - \frac{2820847}{37818}e^{2} - \frac{234385}{1719}e - \frac{229210}{6303}$ |
| 41 | $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ | $-\frac{31895}{151272}e^{7} + \frac{39863}{75636}e^{6} + \frac{1333985}{151272}e^{5} - \frac{16607}{1146}e^{4} - \frac{1215619}{13752}e^{3} + \frac{3162167}{37818}e^{2} + \frac{702883}{3438}e + \frac{436265}{6303}$ |
| 43 | $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ | $-\frac{69}{1528}e^{7} + \frac{257}{2292}e^{6} + \frac{2883}{1528}e^{5} - \frac{3595}{1146}e^{4} - \frac{85421}{4584}e^{3} + \frac{7399}{382}e^{2} + \frac{45767}{1146}e + \frac{2697}{191}$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ | $-1$ |
| 49 | $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ | $\phantom{-}\frac{8267}{50424}e^{7} - \frac{890}{2101}e^{6} - \frac{343457}{50424}e^{5} + \frac{27023}{2292}e^{4} + \frac{103049}{1528}e^{3} - \frac{1750171}{25212}e^{2} - \frac{28923}{191}e - \frac{100281}{2101}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{13501}{75636}e^{7} - \frac{32357}{75636}e^{6} - \frac{564871}{75636}e^{5} + \frac{26495}{2292}e^{4} + \frac{511865}{6876}e^{3} - \frac{5051335}{75636}e^{2} - \frac{589033}{3438}e - \frac{350408}{6303}$ |
| 71 | $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ | $-\frac{778}{18909}e^{7} + \frac{1739}{18909}e^{6} + \frac{67613}{37818}e^{5} - \frac{1426}{573}e^{4} - \frac{33524}{1719}e^{3} + \frac{542345}{37818}e^{2} + \frac{95798}{1719}e + \frac{110750}{6303}$ |
| 71 | $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ | $-\frac{965}{75636}e^{7} - \frac{395}{75636}e^{6} + \frac{46781}{75636}e^{5} + \frac{1519}{2292}e^{4} - \frac{53005}{6876}e^{3} - \frac{691795}{75636}e^{2} + \frac{46780}{1719}e + \frac{144568}{6303}$ |
| 83 | $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ | $\phantom{-}\frac{1193}{37818}e^{7} - \frac{2059}{37818}e^{6} - \frac{26497}{18909}e^{5} + \frac{661}{573}e^{4} + \frac{27104}{1719}e^{3} - \frac{67475}{37818}e^{2} - \frac{81989}{1719}e - \frac{201632}{6303}$ |
| 83 | $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ | $-\frac{2661}{16808}e^{7} + \frac{8267}{25212}e^{6} + \frac{114007}{16808}e^{5} - \frac{9347}{1146}e^{4} - \frac{324547}{4584}e^{3} + \frac{82943}{2101}e^{2} + \frac{210445}{1146}e + \frac{162473}{2101}$ |
| 97 | $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ | $\phantom{-}\frac{727}{37818}e^{7} - \frac{29}{37818}e^{6} - \frac{18572}{18909}e^{5} - \frac{183}{382}e^{4} + \frac{46547}{3438}e^{3} + \frac{147379}{18909}e^{2} - \frac{92746}{1719}e - \frac{176128}{6303}$ |
| 97 | $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ | $\phantom{-}\frac{727}{37818}e^{7} - \frac{29}{37818}e^{6} - \frac{18572}{18909}e^{5} - \frac{183}{382}e^{4} + \frac{46547}{3438}e^{3} + \frac{147379}{18909}e^{2} - \frac{92746}{1719}e - \frac{176128}{6303}$ |
| 113 | $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ | $-\frac{11309}{18909}e^{7} + \frac{57005}{37818}e^{6} + \frac{940945}{37818}e^{5} - \frac{15877}{382}e^{4} - \frac{423457}{1719}e^{3} + \frac{4611341}{18909}e^{2} + \frac{953041}{1719}e + \frac{1131562}{6303}$ |
| 113 | $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ | $-\frac{3539}{25212}e^{7} + \frac{1796}{6303}e^{6} + \frac{151589}{25212}e^{5} - \frac{3998}{573}e^{4} - \frac{143705}{2292}e^{3} + \frac{206312}{6303}e^{2} + \frac{94298}{573}e + \frac{153544}{2101}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $43$ | $[43,43,w^{5} - 7w^{3} - w^{2} + 10w + 3]$ | $1$ |