Properties

Label 19.12.a
Level 19
Weight 12
Character orbit a
Rep. character \(\chi_{19}(1,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 2
Sturm bound 20
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 19.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(19))\).

Total New Old
Modular forms 20 16 4
Cusp forms 18 16 2
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.
\(+\)\(9\)
\(-\)\(7\)

Trace form

\(16q \) \(\mathstrut +\mathstrut 78q^{2} \) \(\mathstrut +\mathstrut 506q^{3} \) \(\mathstrut +\mathstrut 18442q^{4} \) \(\mathstrut -\mathstrut 12193q^{5} \) \(\mathstrut +\mathstrut 17746q^{6} \) \(\mathstrut -\mathstrut 21289q^{7} \) \(\mathstrut -\mathstrut 149592q^{8} \) \(\mathstrut +\mathstrut 979300q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 78q^{2} \) \(\mathstrut +\mathstrut 506q^{3} \) \(\mathstrut +\mathstrut 18442q^{4} \) \(\mathstrut -\mathstrut 12193q^{5} \) \(\mathstrut +\mathstrut 17746q^{6} \) \(\mathstrut -\mathstrut 21289q^{7} \) \(\mathstrut -\mathstrut 149592q^{8} \) \(\mathstrut +\mathstrut 979300q^{9} \) \(\mathstrut +\mathstrut 341688q^{10} \) \(\mathstrut -\mathstrut 1223717q^{11} \) \(\mathstrut +\mathstrut 3492360q^{12} \) \(\mathstrut -\mathstrut 1830142q^{13} \) \(\mathstrut +\mathstrut 838540q^{14} \) \(\mathstrut -\mathstrut 6233230q^{15} \) \(\mathstrut +\mathstrut 17679994q^{16} \) \(\mathstrut +\mathstrut 3402101q^{17} \) \(\mathstrut +\mathstrut 24242358q^{18} \) \(\mathstrut -\mathstrut 4952198q^{19} \) \(\mathstrut -\mathstrut 60129752q^{20} \) \(\mathstrut +\mathstrut 23771926q^{21} \) \(\mathstrut -\mathstrut 32921424q^{22} \) \(\mathstrut -\mathstrut 2365496q^{23} \) \(\mathstrut +\mathstrut 181367310q^{24} \) \(\mathstrut +\mathstrut 158507947q^{25} \) \(\mathstrut -\mathstrut 42768310q^{26} \) \(\mathstrut +\mathstrut 353249516q^{27} \) \(\mathstrut -\mathstrut 319434562q^{28} \) \(\mathstrut -\mathstrut 325489264q^{29} \) \(\mathstrut +\mathstrut 8327804q^{30} \) \(\mathstrut -\mathstrut 118517044q^{31} \) \(\mathstrut +\mathstrut 985456272q^{32} \) \(\mathstrut -\mathstrut 550268602q^{33} \) \(\mathstrut -\mathstrut 157690308q^{34} \) \(\mathstrut -\mathstrut 810439815q^{35} \) \(\mathstrut +\mathstrut 609704716q^{36} \) \(\mathstrut +\mathstrut 98876252q^{37} \) \(\mathstrut -\mathstrut 237705504q^{38} \) \(\mathstrut -\mathstrut 515081352q^{39} \) \(\mathstrut -\mathstrut 3300258804q^{40} \) \(\mathstrut -\mathstrut 67663120q^{41} \) \(\mathstrut -\mathstrut 430356238q^{42} \) \(\mathstrut -\mathstrut 450115753q^{43} \) \(\mathstrut -\mathstrut 1972092304q^{44} \) \(\mathstrut -\mathstrut 1066438561q^{45} \) \(\mathstrut +\mathstrut 6831031716q^{46} \) \(\mathstrut -\mathstrut 5451652275q^{47} \) \(\mathstrut +\mathstrut 146638560q^{48} \) \(\mathstrut +\mathstrut 10657053615q^{49} \) \(\mathstrut +\mathstrut 6593825954q^{50} \) \(\mathstrut +\mathstrut 5342120518q^{51} \) \(\mathstrut -\mathstrut 12611576500q^{52} \) \(\mathstrut +\mathstrut 5011589674q^{53} \) \(\mathstrut -\mathstrut 4624964354q^{54} \) \(\mathstrut -\mathstrut 10374837615q^{55} \) \(\mathstrut +\mathstrut 12333026196q^{56} \) \(\mathstrut -\mathstrut 1203384114q^{57} \) \(\mathstrut +\mathstrut 24172387026q^{58} \) \(\mathstrut +\mathstrut 21182158366q^{59} \) \(\mathstrut -\mathstrut 26944821620q^{60} \) \(\mathstrut -\mathstrut 9408922813q^{61} \) \(\mathstrut +\mathstrut 10328194276q^{62} \) \(\mathstrut -\mathstrut 33056103849q^{63} \) \(\mathstrut +\mathstrut 9781552066q^{64} \) \(\mathstrut +\mathstrut 5512189248q^{65} \) \(\mathstrut +\mathstrut 10593590924q^{66} \) \(\mathstrut +\mathstrut 8921115440q^{67} \) \(\mathstrut -\mathstrut 80270105486q^{68} \) \(\mathstrut -\mathstrut 35689979712q^{69} \) \(\mathstrut -\mathstrut 12237021204q^{70} \) \(\mathstrut +\mathstrut 30429222702q^{71} \) \(\mathstrut +\mathstrut 112867048440q^{72} \) \(\mathstrut +\mathstrut 16481694089q^{73} \) \(\mathstrut -\mathstrut 32312582600q^{74} \) \(\mathstrut +\mathstrut 119964040516q^{75} \) \(\mathstrut -\mathstrut 12677626880q^{76} \) \(\mathstrut +\mathstrut 80851580935q^{77} \) \(\mathstrut -\mathstrut 94915820300q^{78} \) \(\mathstrut -\mathstrut 70851440296q^{79} \) \(\mathstrut -\mathstrut 209151419180q^{80} \) \(\mathstrut -\mathstrut 8024115980q^{81} \) \(\mathstrut -\mathstrut 135136104444q^{82} \) \(\mathstrut -\mathstrut 71467960000q^{83} \) \(\mathstrut +\mathstrut 102342352212q^{84} \) \(\mathstrut +\mathstrut 284747028969q^{85} \) \(\mathstrut -\mathstrut 55245452724q^{86} \) \(\mathstrut -\mathstrut 46540227372q^{87} \) \(\mathstrut -\mathstrut 290089047288q^{88} \) \(\mathstrut +\mathstrut 102444897902q^{89} \) \(\mathstrut -\mathstrut 116755846180q^{90} \) \(\mathstrut +\mathstrut 232285890436q^{91} \) \(\mathstrut +\mathstrut 207214577930q^{92} \) \(\mathstrut -\mathstrut 171735098424q^{93} \) \(\mathstrut +\mathstrut 437130137688q^{94} \) \(\mathstrut -\mathstrut 40660021679q^{95} \) \(\mathstrut +\mathstrut 717917414798q^{96} \) \(\mathstrut -\mathstrut 328812992134q^{97} \) \(\mathstrut -\mathstrut 637037356106q^{98} \) \(\mathstrut -\mathstrut 203910655757q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(19))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19
19.12.a.a \(7\) \(14.599\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-9\) \(10\) \(-14307\) \(-2209\) \(-\) \(q+(-1-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{4})q^{3}+\cdots\)
19.12.a.b \(9\) \(14.599\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(87\) \(496\) \(2114\) \(-19080\) \(+\) \(q+(10-\beta _{1})q^{2}+(56-3\beta _{1}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(19))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(19)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)