Base field \(\Q(\sqrt{241}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[10, 10, 3w + 22]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} - 5x^{11} - 4x^{10} + 52x^{9} - 35x^{8} - 164x^{7} + 189x^{6} + 166x^{5} - 230x^{4} - 70x^{3} + 94x^{2} + 12x - 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -393w - 2854]$ | $\phantom{-}1$ |
2 | $[2, 2, -393w + 3247]$ | $\phantom{-}e$ |
3 | $[3, 3, 4w - 33]$ | $-\frac{7}{3}e^{11} + \frac{29}{3}e^{10} + \frac{46}{3}e^{9} - \frac{295}{3}e^{8} + \frac{32}{3}e^{7} + \frac{881}{3}e^{6} - 162e^{5} - \frac{742}{3}e^{4} + \frac{362}{3}e^{3} + \frac{211}{3}e^{2} - \frac{46}{3}e - 4$ |
3 | $[3, 3, 4w + 29]$ | $-\frac{8}{3}e^{11} + \frac{31}{3}e^{10} + \frac{62}{3}e^{9} - \frac{326}{3}e^{8} - \frac{56}{3}e^{7} + \frac{1045}{3}e^{6} - 100e^{5} - \frac{1070}{3}e^{4} + \frac{250}{3}e^{3} + \frac{383}{3}e^{2} - \frac{20}{3}e - 9$ |
5 | $[5, 5, 42w + 305]$ | $\phantom{-}\frac{4}{3}e^{11} - \frac{17}{3}e^{10} - \frac{25}{3}e^{9} + \frac{172}{3}e^{8} - \frac{29}{3}e^{7} - \frac{509}{3}e^{6} + 98e^{5} + \frac{424}{3}e^{4} - \frac{179}{3}e^{3} - \frac{139}{3}e^{2} + \frac{1}{3}e + 5$ |
5 | $[5, 5, -42w + 347]$ | $\phantom{-}1$ |
29 | $[29, 29, 1820w + 13217]$ | $\phantom{-}4e^{11} - 17e^{10} - 24e^{9} + 169e^{8} - 39e^{7} - 477e^{6} + 322e^{5} + 322e^{4} - 196e^{3} - 46e^{2} + 3e - 2$ |
29 | $[29, 29, 1820w - 15037]$ | $-2e^{11} + 8e^{10} + 15e^{9} - 85e^{8} - 8e^{7} + 279e^{6} - 98e^{5} - 307e^{4} + 91e^{3} + 132e^{2} - 7e - 16$ |
41 | $[41, 41, -80w - 581]$ | $\phantom{-}\frac{4}{3}e^{11} - \frac{14}{3}e^{10} - \frac{37}{3}e^{9} + \frac{154}{3}e^{8} + \frac{85}{3}e^{7} - \frac{536}{3}e^{6} + 2e^{5} + \frac{646}{3}e^{4} - \frac{77}{3}e^{3} - \frac{241}{3}e^{2} + \frac{46}{3}e + 3$ |
41 | $[41, 41, 80w - 661]$ | $-\frac{7}{3}e^{11} + \frac{23}{3}e^{10} + \frac{73}{3}e^{9} - \frac{265}{3}e^{8} - \frac{235}{3}e^{7} + \frac{1004}{3}e^{6} + 88e^{5} - \frac{1441}{3}e^{4} - \frac{151}{3}e^{3} + \frac{742}{3}e^{2} + \frac{50}{3}e - 27$ |
47 | $[47, 47, 34w - 281]$ | $\phantom{-}\frac{49}{3}e^{11} - \frac{179}{3}e^{10} - \frac{424}{3}e^{9} + \frac{1918}{3}e^{8} + \frac{802}{3}e^{7} - \frac{6377}{3}e^{6} + 140e^{5} + \frac{7102}{3}e^{4} - \frac{269}{3}e^{3} - \frac{2782}{3}e^{2} - \frac{158}{3}e + 79$ |
47 | $[47, 47, 34w + 247]$ | $\phantom{-}\frac{23}{3}e^{11} - \frac{70}{3}e^{10} - \frac{260}{3}e^{9} + \frac{824}{3}e^{8} + \frac{977}{3}e^{7} - \frac{3214}{3}e^{6} - 489e^{5} + \frac{4745}{3}e^{4} + \frac{935}{3}e^{3} - \frac{2324}{3}e^{2} - \frac{223}{3}e + 82$ |
49 | $[49, 7, -7]$ | $\phantom{-}\frac{5}{3}e^{11} - \frac{37}{3}e^{10} + \frac{37}{3}e^{9} + \frac{305}{3}e^{8} - \frac{715}{3}e^{7} - \frac{433}{3}e^{6} + 763e^{5} - \frac{913}{3}e^{4} - \frac{1552}{3}e^{3} + \frac{823}{3}e^{2} + \frac{227}{3}e - 32$ |
53 | $[53, 53, 6w + 43]$ | $\phantom{-}\frac{35}{3}e^{11} - \frac{136}{3}e^{10} - \frac{269}{3}e^{9} + \frac{1424}{3}e^{8} + \frac{230}{3}e^{7} - \frac{4528}{3}e^{6} + 436e^{5} + \frac{4571}{3}e^{4} - \frac{982}{3}e^{3} - \frac{1694}{3}e^{2} + \frac{68}{3}e + 50$ |
53 | $[53, 53, 6w - 49]$ | $\phantom{-}\frac{32}{3}e^{11} - \frac{127}{3}e^{10} - \frac{236}{3}e^{9} + \frac{1319}{3}e^{8} + \frac{116}{3}e^{7} - \frac{4123}{3}e^{6} + 477e^{5} + \frac{3983}{3}e^{4} - \frac{967}{3}e^{3} - \frac{1421}{3}e^{2} + \frac{8}{3}e + 42$ |
59 | $[59, 59, 10w + 73]$ | $-\frac{8}{3}e^{11} + \frac{40}{3}e^{10} + \frac{23}{3}e^{9} - \frac{377}{3}e^{8} + \frac{331}{3}e^{7} + \frac{925}{3}e^{6} - 464e^{5} - \frac{236}{3}e^{4} + \frac{1000}{3}e^{3} - \frac{190}{3}e^{2} - \frac{146}{3}e + 15$ |
59 | $[59, 59, 10w - 83]$ | $-\frac{17}{3}e^{11} + \frac{73}{3}e^{10} + \frac{98}{3}e^{9} - \frac{722}{3}e^{8} + \frac{208}{3}e^{7} + \frac{2014}{3}e^{6} - 503e^{5} - \frac{1298}{3}e^{4} + \frac{1006}{3}e^{3} + \frac{167}{3}e^{2} - \frac{116}{3}e + 3$ |
61 | $[61, 61, 4178w + 30341]$ | $\phantom{-}\frac{26}{3}e^{11} - \frac{79}{3}e^{10} - \frac{293}{3}e^{9} + \frac{923}{3}e^{8} + \frac{1103}{3}e^{7} - \frac{3559}{3}e^{6} - 567e^{5} + \frac{5165}{3}e^{4} + \frac{1202}{3}e^{3} - \frac{2492}{3}e^{2} - \frac{319}{3}e + 89$ |
61 | $[61, 61, 4178w - 34519]$ | $-\frac{29}{3}e^{11} + \frac{100}{3}e^{10} + \frac{275}{3}e^{9} - \frac{1097}{3}e^{8} - \frac{716}{3}e^{7} + \frac{3814}{3}e^{6} + 150e^{5} - \frac{4676}{3}e^{4} - \frac{365}{3}e^{3} + \frac{2057}{3}e^{2} + \frac{178}{3}e - 69$ |
67 | $[67, 67, -332w + 2743]$ | $\phantom{-}\frac{43}{3}e^{11} - \frac{146}{3}e^{10} - \frac{424}{3}e^{9} + \frac{1633}{3}e^{8} + \frac{1213}{3}e^{7} - \frac{5870}{3}e^{6} - 343e^{5} + \frac{7627}{3}e^{4} + \frac{622}{3}e^{3} - \frac{3448}{3}e^{2} - \frac{257}{3}e + 116$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -393w - 2854]$ | $-1$ |
$5$ | $[5, 5, -42w + 347]$ | $-1$ |