Properties

Label 19.3.d
Level 19
Weight 3
Character orbit d
Rep. character \(\chi_{19}(8,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 6
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 19.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q(\zeta_{6})\)
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 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\(6q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 14q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 14q^{9} \) \(\mathstrut -\mathstrut 60q^{10} \) \(\mathstrut +\mathstrut 26q^{11} \) \(\mathstrut +\mathstrut 30q^{13} \) \(\mathstrut +\mathstrut 54q^{14} \) \(\mathstrut -\mathstrut 18q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut 42q^{17} \) \(\mathstrut +\mathstrut 25q^{19} \) \(\mathstrut +\mathstrut 108q^{20} \) \(\mathstrut -\mathstrut 102q^{21} \) \(\mathstrut -\mathstrut 39q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 83q^{24} \) \(\mathstrut -\mathstrut 17q^{25} \) \(\mathstrut -\mathstrut 148q^{26} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 304q^{30} \) \(\mathstrut +\mathstrut 51q^{32} \) \(\mathstrut +\mathstrut 123q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut -\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut -\mathstrut 96q^{40} \) \(\mathstrut +\mathstrut 63q^{41} \) \(\mathstrut -\mathstrut 92q^{42} \) \(\mathstrut -\mathstrut 34q^{43} \) \(\mathstrut -\mathstrut 69q^{44} \) \(\mathstrut -\mathstrut 28q^{45} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut -\mathstrut 147q^{48} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 132q^{51} \) \(\mathstrut +\mathstrut 162q^{52} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 172q^{58} \) \(\mathstrut -\mathstrut 147q^{59} \) \(\mathstrut -\mathstrut 222q^{60} \) \(\mathstrut +\mathstrut 58q^{61} \) \(\mathstrut -\mathstrut 116q^{62} \) \(\mathstrut +\mathstrut 86q^{63} \) \(\mathstrut +\mathstrut 166q^{64} \) \(\mathstrut +\mathstrut 11q^{66} \) \(\mathstrut +\mathstrut 201q^{67} \) \(\mathstrut -\mathstrut 84q^{68} \) \(\mathstrut -\mathstrut 198q^{70} \) \(\mathstrut -\mathstrut 102q^{71} \) \(\mathstrut +\mathstrut 210q^{72} \) \(\mathstrut +\mathstrut 7q^{73} \) \(\mathstrut +\mathstrut 174q^{74} \) \(\mathstrut -\mathstrut 173q^{76} \) \(\mathstrut -\mathstrut 376q^{77} \) \(\mathstrut +\mathstrut 450q^{78} \) \(\mathstrut +\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 253q^{81} \) \(\mathstrut -\mathstrut 145q^{82} \) \(\mathstrut +\mathstrut 146q^{83} \) \(\mathstrut -\mathstrut 90q^{85} \) \(\mathstrut -\mathstrut 270q^{86} \) \(\mathstrut -\mathstrut 568q^{87} \) \(\mathstrut -\mathstrut 72q^{89} \) \(\mathstrut -\mathstrut 438q^{90} \) \(\mathstrut -\mathstrut 216q^{91} \) \(\mathstrut +\mathstrut 72q^{92} \) \(\mathstrut -\mathstrut 160q^{93} \) \(\mathstrut +\mathstrut 558q^{95} \) \(\mathstrut +\mathstrut 126q^{96} \) \(\mathstrut +\mathstrut 21q^{97} \) \(\mathstrut +\mathstrut 411q^{98} \) \(\mathstrut -\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(6\) \(0.518\) 6.0.6967728.1 None \(-3\) \(-9\) \(-2\) \(0\) \(q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots\)