Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 19
Level $[19,19,w - 1]$
Label 4.4.11525.1-19.4-c
Dimension 10
CM no
Base change no

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Base field 4.4.11525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[19,19,w - 1]$
Label 4.4.11525.1-19.4-c
Dimension 10
Is CM no
Is base change no
Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} \) \(\mathstrut -\mathstrut 12x^{9} \) \(\mathstrut +\mathstrut 35x^{8} \) \(\mathstrut +\mathstrut 96x^{7} \) \(\mathstrut -\mathstrut 618x^{6} \) \(\mathstrut +\mathstrut 354x^{5} \) \(\mathstrut +\mathstrut 2511x^{4} \) \(\mathstrut -\mathstrut 3572x^{3} \) \(\mathstrut -\mathstrut 2269x^{2} \) \(\mathstrut +\mathstrut 5886x \) \(\mathstrut -\mathstrut 2268\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-\frac{317}{1044}e^{9} + \frac{347}{116}e^{8} - \frac{2297}{522}e^{7} - \frac{6305}{174}e^{6} + \frac{8929}{87}e^{5} + \frac{17357}{174}e^{4} - \frac{52437}{116}e^{3} + \frac{29131}{1044}e^{2} + \frac{289897}{522}e - \frac{7790}{29}$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $-\frac{95}{232}e^{9} + \frac{2747}{696}e^{8} - \frac{446}{87}e^{7} - \frac{2915}{58}e^{6} + \frac{15297}{116}e^{5} + \frac{9161}{58}e^{4} - \frac{143341}{232}e^{3} - \frac{3453}{232}e^{2} + \frac{284479}{348}e - \frac{21827}{58}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $-\frac{437}{2088}e^{9} + \frac{1453}{696}e^{8} - \frac{1795}{522}e^{7} - \frac{2027}{87}e^{6} + \frac{25091}{348}e^{5} + \frac{4223}{87}e^{4} - \frac{66579}{232}e^{3} + \frac{115753}{2088}e^{2} + \frac{318871}{1044}e - \frac{8711}{58}$
16 $[16, 2, 2]$ $-\frac{215}{2088}e^{9} + \frac{267}{232}e^{8} - \frac{803}{261}e^{7} - \frac{1327}{174}e^{6} + \frac{15203}{348}e^{5} - \frac{2473}{87}e^{4} - \frac{22329}{232}e^{3} + \frac{266797}{2088}e^{2} - \frac{28817}{1044}e - \frac{269}{58}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $\phantom{-}\frac{311}{2088}e^{9} - \frac{887}{696}e^{8} + \frac{122}{261}e^{7} + \frac{3475}{174}e^{6} - \frac{12011}{348}e^{5} - \frac{16009}{174}e^{4} + \frac{49581}{232}e^{3} + \frac{189977}{2088}e^{2} - \frac{368845}{1044}e + \frac{8395}{58}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $-\frac{421}{2088}e^{9} + \frac{1255}{696}e^{8} - \frac{286}{261}e^{7} - \frac{2428}{87}e^{6} + \frac{18895}{348}e^{5} + \frac{21875}{174}e^{4} - \frac{75783}{232}e^{3} - \frac{233809}{2088}e^{2} + \frac{554687}{1044}e - \frac{12915}{58}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $-\frac{100}{261}e^{9} + \frac{1325}{348}e^{8} - \frac{3295}{522}e^{7} - \frac{3614}{87}e^{6} + \frac{11243}{87}e^{5} + \frac{13849}{174}e^{4} - \frac{28645}{58}e^{3} + \frac{111695}{1044}e^{2} + \frac{128011}{261}e - \frac{6869}{29}$
19 $[19, 19, w - 1]$ $-1$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{19}{696}e^{9} - \frac{187}{696}e^{8} + \frac{80}{87}e^{7} - \frac{57}{58}e^{6} - \frac{695}{116}e^{5} + \frac{1018}{29}e^{4} - \frac{10713}{232}e^{3} - \frac{49085}{696}e^{2} + \frac{59501}{348}e - \frac{4109}{58}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}\frac{79}{348}e^{9} - \frac{689}{348}e^{8} + \frac{37}{58}e^{7} + \frac{1933}{58}e^{6} - \frac{1699}{29}e^{5} - \frac{9601}{58}e^{4} + \frac{46141}{116}e^{3} + \frac{57331}{348}e^{2} - \frac{40453}{58}e + \frac{8742}{29}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-\frac{80}{261}e^{9} + \frac{973}{348}e^{8} - \frac{535}{261}e^{7} - \frac{3709}{87}e^{6} + \frac{7672}{87}e^{5} + \frac{32429}{174}e^{4} - \frac{30253}{58}e^{3} - \frac{147893}{1044}e^{2} + \frac{441649}{522}e - \frac{10982}{29}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}\frac{977}{2088}e^{9} - \frac{3191}{696}e^{8} + \frac{1580}{261}e^{7} + \frac{5219}{87}e^{6} - \frac{54899}{348}e^{5} - \frac{34957}{174}e^{4} + \frac{176995}{232}e^{3} + \frac{97097}{2088}e^{2} - \frac{1090879}{1044}e + \frac{27805}{58}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $-\frac{1175}{2088}e^{9} + \frac{1211}{232}e^{8} - \frac{2167}{522}e^{7} - \frac{13933}{174}e^{6} + \frac{59147}{348}e^{5} + \frac{30701}{87}e^{4} - \frac{233369}{232}e^{3} - \frac{562379}{2088}e^{2} + \frac{1698853}{1044}e - \frac{42321}{58}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $-\frac{67}{696}e^{9} + \frac{173}{232}e^{8} + \frac{14}{87}e^{7} - \frac{349}{29}e^{6} + \frac{1709}{116}e^{5} + \frac{3381}{58}e^{4} - \frac{23379}{232}e^{3} - \frac{48715}{696}e^{2} + \frac{61001}{348}e - \frac{3527}{58}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}\frac{235}{348}e^{9} - \frac{2261}{348}e^{8} + \frac{519}{58}e^{7} + \frac{4535}{58}e^{6} - \frac{6167}{29}e^{5} - \frac{12375}{58}e^{4} + \frac{106393}{116}e^{3} - \frac{14753}{348}e^{2} - \frac{63315}{58}e + \frac{14622}{29}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $-\frac{775}{1044}e^{9} + \frac{1241}{174}e^{8} - \frac{2216}{261}e^{7} - \frac{16723}{174}e^{6} + \frac{20897}{87}e^{5} + \frac{29639}{87}e^{4} - \frac{140293}{116}e^{3} - \frac{60899}{522}e^{2} + \frac{899429}{522}e - \frac{22779}{29}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}\frac{17}{522}e^{9} - \frac{127}{174}e^{8} + \frac{1109}{261}e^{7} - \frac{407}{174}e^{6} - \frac{7555}{174}e^{5} + \frac{16901}{174}e^{4} + \frac{1030}{29}e^{3} - \frac{66281}{261}e^{2} + \frac{94297}{522}e - \frac{509}{29}$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}\frac{1063}{2088}e^{9} - \frac{3349}{696}e^{8} + \frac{2567}{522}e^{7} + \frac{11891}{174}e^{6} - \frac{55099}{348}e^{5} - \frac{23371}{87}e^{4} + \frac{196529}{232}e^{3} + \frac{334063}{2088}e^{2} - \frac{1326641}{1044}e + \frac{32599}{58}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $-\frac{719}{2088}e^{9} + \frac{809}{232}e^{8} - \frac{3199}{522}e^{7} - \frac{3257}{87}e^{6} + \frac{42293}{348}e^{5} + \frac{5804}{87}e^{4} - \frac{106329}{232}e^{3} + \frac{231175}{2088}e^{2} + \frac{464329}{1044}e - \frac{12901}{58}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,w - 1]$ $1$