Properties

Label 19.3.f
Level 19
Weight 3
Character orbit f
Rep. character \(\chi_{19}(2,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 12
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 19.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(19, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 12 12 0
Eisenstein series 12 12 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 36q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 36q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut 51q^{10} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 63q^{12} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 63q^{15} \) \(\mathstrut -\mathstrut 12q^{16} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 24q^{19} \) \(\mathstrut -\mathstrut 90q^{20} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 78q^{22} \) \(\mathstrut -\mathstrut 102q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut -\mathstrut 156q^{25} \) \(\mathstrut +\mathstrut 21q^{26} \) \(\mathstrut -\mathstrut 27q^{27} \) \(\mathstrut +\mathstrut 12q^{28} \) \(\mathstrut +\mathstrut 147q^{29} \) \(\mathstrut +\mathstrut 24q^{30} \) \(\mathstrut +\mathstrut 99q^{31} \) \(\mathstrut +\mathstrut 165q^{32} \) \(\mathstrut +\mathstrut 84q^{33} \) \(\mathstrut +\mathstrut 132q^{34} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut +\mathstrut 63q^{36} \) \(\mathstrut +\mathstrut 72q^{38} \) \(\mathstrut -\mathstrut 108q^{39} \) \(\mathstrut -\mathstrut 138q^{40} \) \(\mathstrut -\mathstrut 144q^{41} \) \(\mathstrut -\mathstrut 237q^{42} \) \(\mathstrut -\mathstrut 27q^{43} \) \(\mathstrut -\mathstrut 123q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 54q^{46} \) \(\mathstrut -\mathstrut 99q^{47} \) \(\mathstrut -\mathstrut 51q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 72q^{50} \) \(\mathstrut -\mathstrut 42q^{51} \) \(\mathstrut +\mathstrut 93q^{52} \) \(\mathstrut +\mathstrut 111q^{53} \) \(\mathstrut +\mathstrut 21q^{54} \) \(\mathstrut +\mathstrut 162q^{55} \) \(\mathstrut -\mathstrut 168q^{57} \) \(\mathstrut -\mathstrut 132q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 30q^{60} \) \(\mathstrut +\mathstrut 150q^{61} \) \(\mathstrut +\mathstrut 108q^{62} \) \(\mathstrut +\mathstrut 234q^{63} \) \(\mathstrut +\mathstrut 27q^{64} \) \(\mathstrut +\mathstrut 126q^{65} \) \(\mathstrut +\mathstrut 168q^{66} \) \(\mathstrut +\mathstrut 135q^{67} \) \(\mathstrut -\mathstrut 30q^{68} \) \(\mathstrut +\mathstrut 72q^{69} \) \(\mathstrut +\mathstrut 225q^{70} \) \(\mathstrut -\mathstrut 168q^{71} \) \(\mathstrut -\mathstrut 102q^{72} \) \(\mathstrut -\mathstrut 90q^{73} \) \(\mathstrut -\mathstrut 231q^{74} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut +\mathstrut 246q^{77} \) \(\mathstrut -\mathstrut 189q^{78} \) \(\mathstrut -\mathstrut 75q^{79} \) \(\mathstrut +\mathstrut 21q^{80} \) \(\mathstrut -\mathstrut 159q^{81} \) \(\mathstrut -\mathstrut 117q^{82} \) \(\mathstrut -\mathstrut 156q^{83} \) \(\mathstrut +\mathstrut 99q^{84} \) \(\mathstrut -\mathstrut 300q^{85} \) \(\mathstrut -\mathstrut 144q^{86} \) \(\mathstrut +\mathstrut 69q^{87} \) \(\mathstrut -\mathstrut 405q^{88} \) \(\mathstrut -\mathstrut 558q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut -\mathstrut 453q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut -\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 69q^{95} \) \(\mathstrut +\mathstrut 558q^{96} \) \(\mathstrut +\mathstrut 465q^{97} \) \(\mathstrut +\mathstrut 777q^{98} \) \(\mathstrut +\mathstrut 462q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(19, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.3.f.a \(12\) \(0.518\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(-6\) \(6\) \(q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)