Properties

Label 19.2.e
Level 19
Weight 2
Character orbit e
Rep. character \(\chi_{19}(4,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 6
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 19.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(19, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

Trace form

\(6q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 9q^{10} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 18q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 15q^{26} \) \(\mathstrut +\mathstrut 6q^{27} \) \(\mathstrut +\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 3q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut -\mathstrut 15q^{45} \) \(\mathstrut -\mathstrut 18q^{46} \) \(\mathstrut -\mathstrut 3q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut +\mathstrut 30q^{54} \) \(\mathstrut +\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 24q^{57} \) \(\mathstrut +\mathstrut 36q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 12q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 30q^{67} \) \(\mathstrut -\mathstrut 15q^{68} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 15q^{74} \) \(\mathstrut +\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 36q^{76} \) \(\mathstrut -\mathstrut 18q^{77} \) \(\mathstrut +\mathstrut 15q^{78} \) \(\mathstrut -\mathstrut 39q^{79} \) \(\mathstrut +\mathstrut 3q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 54q^{82} \) \(\mathstrut +\mathstrut 3q^{84} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 21q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 18q^{90} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut +\mathstrut 42q^{92} \) \(\mathstrut +\mathstrut 9q^{93} \) \(\mathstrut +\mathstrut 18q^{94} \) \(\mathstrut +\mathstrut 39q^{95} \) \(\mathstrut +\mathstrut 18q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 9q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(19, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.2.e.a \(6\) \(0.152\) \(\Q(\zeta_{18})\) None \(-6\) \(-3\) \(-6\) \(0\) \(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)