Properties

Label 19.10.a
Level 19
Weight 10
Character orbit a
Rep. character \(\chi_{19}(1,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 2
Sturm bound 16
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 19.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(19))\).

Total New Old
Modular forms 16 14 2
Cusp forms 14 14 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(19\)Dim.
\(+\)\(6\)
\(-\)\(8\)

Trace form

\(14q \) \(\mathstrut -\mathstrut 18q^{2} \) \(\mathstrut -\mathstrut 148q^{3} \) \(\mathstrut +\mathstrut 4010q^{4} \) \(\mathstrut +\mathstrut 282q^{5} \) \(\mathstrut -\mathstrut 4142q^{6} \) \(\mathstrut -\mathstrut 3048q^{7} \) \(\mathstrut -\mathstrut 12600q^{8} \) \(\mathstrut +\mathstrut 120340q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut -\mathstrut 18q^{2} \) \(\mathstrut -\mathstrut 148q^{3} \) \(\mathstrut +\mathstrut 4010q^{4} \) \(\mathstrut +\mathstrut 282q^{5} \) \(\mathstrut -\mathstrut 4142q^{6} \) \(\mathstrut -\mathstrut 3048q^{7} \) \(\mathstrut -\mathstrut 12600q^{8} \) \(\mathstrut +\mathstrut 120340q^{9} \) \(\mathstrut +\mathstrut 19288q^{10} \) \(\mathstrut +\mathstrut 103506q^{11} \) \(\mathstrut -\mathstrut 111048q^{12} \) \(\mathstrut -\mathstrut 82456q^{13} \) \(\mathstrut -\mathstrut 393732q^{14} \) \(\mathstrut +\mathstrut 130904q^{15} \) \(\mathstrut +\mathstrut 1604282q^{16} \) \(\mathstrut +\mathstrut 295380q^{17} \) \(\mathstrut -\mathstrut 850698q^{18} \) \(\mathstrut +\mathstrut 260642q^{19} \) \(\mathstrut +\mathstrut 1640232q^{20} \) \(\mathstrut -\mathstrut 2888000q^{21} \) \(\mathstrut +\mathstrut 2466944q^{22} \) \(\mathstrut -\mathstrut 2343102q^{23} \) \(\mathstrut -\mathstrut 1921554q^{24} \) \(\mathstrut +\mathstrut 7332216q^{25} \) \(\mathstrut +\mathstrut 3572826q^{26} \) \(\mathstrut -\mathstrut 11407192q^{27} \) \(\mathstrut +\mathstrut 9077678q^{28} \) \(\mathstrut -\mathstrut 2632332q^{29} \) \(\mathstrut -\mathstrut 22890244q^{30} \) \(\mathstrut -\mathstrut 12588132q^{31} \) \(\mathstrut -\mathstrut 21162528q^{32} \) \(\mathstrut +\mathstrut 31551428q^{33} \) \(\mathstrut -\mathstrut 22374980q^{34} \) \(\mathstrut +\mathstrut 11467278q^{35} \) \(\mathstrut +\mathstrut 19825948q^{36} \) \(\mathstrut +\mathstrut 8798496q^{37} \) \(\mathstrut +\mathstrut 6255408q^{38} \) \(\mathstrut -\mathstrut 26244450q^{39} \) \(\mathstrut +\mathstrut 35716620q^{40} \) \(\mathstrut +\mathstrut 9917640q^{41} \) \(\mathstrut +\mathstrut 8826002q^{42} \) \(\mathstrut -\mathstrut 38494406q^{43} \) \(\mathstrut +\mathstrut 120967968q^{44} \) \(\mathstrut +\mathstrut 47802638q^{45} \) \(\mathstrut -\mathstrut 151614364q^{46} \) \(\mathstrut -\mathstrut 73866414q^{47} \) \(\mathstrut +\mathstrut 141647088q^{48} \) \(\mathstrut +\mathstrut 132775106q^{49} \) \(\mathstrut +\mathstrut 191811234q^{50} \) \(\mathstrut -\mathstrut 25081076q^{51} \) \(\mathstrut -\mathstrut 111826308q^{52} \) \(\mathstrut -\mathstrut 124055520q^{53} \) \(\mathstrut -\mathstrut 184629938q^{54} \) \(\mathstrut +\mathstrut 260022402q^{55} \) \(\mathstrut -\mathstrut 699193500q^{56} \) \(\mathstrut +\mathstrut 21112002q^{57} \) \(\mathstrut -\mathstrut 385408766q^{58} \) \(\mathstrut +\mathstrut 13405548q^{59} \) \(\mathstrut +\mathstrut 375959116q^{60} \) \(\mathstrut +\mathstrut 372498678q^{61} \) \(\mathstrut +\mathstrut 113577396q^{62} \) \(\mathstrut +\mathstrut 455976042q^{63} \) \(\mathstrut +\mathstrut 348050162q^{64} \) \(\mathstrut -\mathstrut 168041796q^{65} \) \(\mathstrut -\mathstrut 1140846148q^{66} \) \(\mathstrut -\mathstrut 14342432q^{67} \) \(\mathstrut +\mathstrut 520247394q^{68} \) \(\mathstrut +\mathstrut 483883740q^{69} \) \(\mathstrut +\mathstrut 176441244q^{70} \) \(\mathstrut +\mathstrut 9161880q^{71} \) \(\mathstrut -\mathstrut 2128825752q^{72} \) \(\mathstrut -\mathstrut 551284400q^{73} \) \(\mathstrut +\mathstrut 1054592664q^{74} \) \(\mathstrut -\mathstrut 527358704q^{75} \) \(\mathstrut +\mathstrut 166810880q^{76} \) \(\mathstrut -\mathstrut 1178671734q^{77} \) \(\mathstrut +\mathstrut 1235054212q^{78} \) \(\mathstrut +\mathstrut 657938172q^{79} \) \(\mathstrut +\mathstrut 604352820q^{80} \) \(\mathstrut +\mathstrut 712299382q^{81} \) \(\mathstrut +\mathstrut 2866982068q^{82} \) \(\mathstrut +\mathstrut 472925340q^{83} \) \(\mathstrut -\mathstrut 3162362940q^{84} \) \(\mathstrut +\mathstrut 365700774q^{85} \) \(\mathstrut -\mathstrut 105075492q^{86} \) \(\mathstrut +\mathstrut 116369070q^{87} \) \(\mathstrut +\mathstrut 194158248q^{88} \) \(\mathstrut -\mathstrut 2555324040q^{89} \) \(\mathstrut +\mathstrut 1864409564q^{90} \) \(\mathstrut -\mathstrut 178213392q^{91} \) \(\mathstrut +\mathstrut 1668121530q^{92} \) \(\mathstrut +\mathstrut 2005379004q^{93} \) \(\mathstrut -\mathstrut 3623996616q^{94} \) \(\mathstrut +\mathstrut 978189426q^{95} \) \(\mathstrut +\mathstrut 1619378942q^{96} \) \(\mathstrut -\mathstrut 777943680q^{97} \) \(\mathstrut -\mathstrut 67154058q^{98} \) \(\mathstrut -\mathstrut 637221746q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(19))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19
19.10.a.a \(6\) \(9.786\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-33\) \(-155\) \(-3612\) \(4085\) \(+\) \(q+(-6+\beta _{1})q^{2}+(-26+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
19.10.a.b \(8\) \(9.786\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(15\) \(7\) \(3894\) \(-7133\) \(-\) \(q+(2-\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+(331+\cdots)q^{4}+\cdots\)