Properties

Label 19.4.a
Level 19
Weight 4
Character orbit a
Rep. character \(\chi_{19}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 19.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(19))\).

Total New Old
Modular forms 6 4 2
Cusp forms 4 4 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.
\(+\)\(3\)
\(-\)\(1\)

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 50q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 50q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 52q^{10} \) \(\mathstrut -\mathstrut 38q^{11} \) \(\mathstrut -\mathstrut 120q^{12} \) \(\mathstrut +\mathstrut 76q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 200q^{15} \) \(\mathstrut -\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 144q^{18} \) \(\mathstrut -\mathstrut 38q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 80q^{21} \) \(\mathstrut +\mathstrut 280q^{22} \) \(\mathstrut +\mathstrut 82q^{23} \) \(\mathstrut -\mathstrut 594q^{24} \) \(\mathstrut -\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 266q^{26} \) \(\mathstrut -\mathstrut 232q^{27} \) \(\mathstrut -\mathstrut 482q^{28} \) \(\mathstrut +\mathstrut 128q^{29} \) \(\mathstrut -\mathstrut 556q^{30} \) \(\mathstrut -\mathstrut 84q^{31} \) \(\mathstrut +\mathstrut 624q^{32} \) \(\mathstrut +\mathstrut 140q^{33} \) \(\mathstrut +\mathstrut 608q^{34} \) \(\mathstrut -\mathstrut 570q^{35} \) \(\mathstrut +\mathstrut 1072q^{36} \) \(\mathstrut -\mathstrut 540q^{37} \) \(\mathstrut -\mathstrut 114q^{38} \) \(\mathstrut -\mathstrut 426q^{39} \) \(\mathstrut -\mathstrut 324q^{40} \) \(\mathstrut +\mathstrut 1196q^{41} \) \(\mathstrut +\mathstrut 1550q^{42} \) \(\mathstrut -\mathstrut 766q^{43} \) \(\mathstrut +\mathstrut 56q^{44} \) \(\mathstrut +\mathstrut 254q^{45} \) \(\mathstrut -\mathstrut 788q^{46} \) \(\mathstrut -\mathstrut 102q^{47} \) \(\mathstrut -\mathstrut 1056q^{48} \) \(\mathstrut -\mathstrut 320q^{49} \) \(\mathstrut -\mathstrut 1696q^{50} \) \(\mathstrut +\mathstrut 652q^{51} \) \(\mathstrut +\mathstrut 708q^{52} \) \(\mathstrut +\mathstrut 1252q^{53} \) \(\mathstrut -\mathstrut 1382q^{54} \) \(\mathstrut +\mathstrut 450q^{55} \) \(\mathstrut -\mathstrut 684q^{56} \) \(\mathstrut -\mathstrut 114q^{57} \) \(\mathstrut +\mathstrut 1394q^{58} \) \(\mathstrut +\mathstrut 460q^{59} \) \(\mathstrut +\mathstrut 1420q^{60} \) \(\mathstrut +\mathstrut 630q^{61} \) \(\mathstrut -\mathstrut 1604q^{62} \) \(\mathstrut -\mathstrut 1326q^{63} \) \(\mathstrut +\mathstrut 274q^{64} \) \(\mathstrut -\mathstrut 372q^{65} \) \(\mathstrut -\mathstrut 1084q^{66} \) \(\mathstrut -\mathstrut 1168q^{67} \) \(\mathstrut -\mathstrut 1622q^{68} \) \(\mathstrut -\mathstrut 108q^{69} \) \(\mathstrut +\mathstrut 2436q^{70} \) \(\mathstrut +\mathstrut 600q^{71} \) \(\mathstrut +\mathstrut 2784q^{72} \) \(\mathstrut +\mathstrut 980q^{73} \) \(\mathstrut -\mathstrut 20q^{74} \) \(\mathstrut +\mathstrut 1936q^{75} \) \(\mathstrut -\mathstrut 380q^{76} \) \(\mathstrut -\mathstrut 506q^{77} \) \(\mathstrut -\mathstrut 1652q^{78} \) \(\mathstrut +\mathstrut 348q^{79} \) \(\mathstrut -\mathstrut 620q^{80} \) \(\mathstrut -\mathstrut 1172q^{81} \) \(\mathstrut +\mathstrut 152q^{82} \) \(\mathstrut -\mathstrut 532q^{83} \) \(\mathstrut +\mathstrut 852q^{84} \) \(\mathstrut -\mathstrut 126q^{85} \) \(\mathstrut +\mathstrut 3180q^{86} \) \(\mathstrut -\mathstrut 426q^{87} \) \(\mathstrut -\mathstrut 792q^{88} \) \(\mathstrut -\mathstrut 340q^{89} \) \(\mathstrut -\mathstrut 1960q^{90} \) \(\mathstrut -\mathstrut 336q^{91} \) \(\mathstrut -\mathstrut 2494q^{92} \) \(\mathstrut +\mathstrut 612q^{93} \) \(\mathstrut +\mathstrut 408q^{94} \) \(\mathstrut -\mathstrut 494q^{95} \) \(\mathstrut +\mathstrut 638q^{96} \) \(\mathstrut -\mathstrut 1692q^{97} \) \(\mathstrut -\mathstrut 1784q^{98} \) \(\mathstrut +\mathstrut 358q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(19))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19
19.4.a.a \(1\) \(1.121\) \(\Q\) None \(-3\) \(-5\) \(-12\) \(11\) \(-\) \(q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots\)
19.4.a.b \(3\) \(1.121\) 3.3.3144.1 None \(3\) \(1\) \(14\) \(-35\) \(+\) \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)