Properties

Label 2.2.241.1-10.2-a
Base field \(\Q(\sqrt{241}) \)
Weight $[2, 2]$
Level norm $10$
Level $[10, 10, 3w + 22]$
Dimension $12$
CM no
Base change no

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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 $[67, 67, -332w + 2743]$ $\phantom{-}\frac{43}{3}e^{11} - \frac{146}{3}e^{10} - \frac{424}{3}e^{9} + \frac{1633}{3}e^{8} + \frac{1213}{3}e^{7} - \frac{5870}{3}e^{6} - 343e^{5} + \frac{7627}{3}e^{4} + \frac{622}{3}e^{3} - \frac{3448}{3}e^{2} - \frac{257}{3}e + 116$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -393w - 2854]$ $-1$
$5$ $[5, 5, -42w + 347]$ $-1$