Properties

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

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 19.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\(3q \) \(\mathstrut -\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 26q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 26q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 74q^{16} \) \(\mathstrut +\mathstrut 45q^{17} \) \(\mathstrut -\mathstrut 31q^{19} \) \(\mathstrut -\mathstrut 108q^{20} \) \(\mathstrut +\mathstrut 40q^{23} \) \(\mathstrut -\mathstrut 130q^{24} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 26q^{26} \) \(\mathstrut +\mathstrut 70q^{28} \) \(\mathstrut +\mathstrut 104q^{30} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 108q^{36} \) \(\mathstrut -\mathstrut 130q^{38} \) \(\mathstrut +\mathstrut 26q^{39} \) \(\mathstrut -\mathstrut 130q^{42} \) \(\mathstrut -\mathstrut 125q^{43} \) \(\mathstrut +\mathstrut 192q^{44} \) \(\mathstrut -\mathstrut 113q^{45} \) \(\mathstrut +\mathstrut 95q^{47} \) \(\mathstrut -\mathstrut 72q^{49} \) \(\mathstrut +\mathstrut 130q^{54} \) \(\mathstrut -\mathstrut 107q^{55} \) \(\mathstrut +\mathstrut 130q^{57} \) \(\mathstrut -\mathstrut 130q^{58} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 260q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 62q^{64} \) \(\mathstrut -\mathstrut 260q^{66} \) \(\mathstrut -\mathstrut 210q^{68} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 156q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 85q^{77} \) \(\mathstrut +\mathstrut 88q^{80} \) \(\mathstrut -\mathstrut 121q^{81} \) \(\mathstrut -\mathstrut 260q^{82} \) \(\mathstrut +\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 130q^{87} \) \(\mathstrut -\mathstrut 750q^{92} \) \(\mathstrut -\mathstrut 260q^{93} \) \(\mathstrut +\mathstrut 123q^{95} \) \(\mathstrut +\mathstrut 234q^{96} \) \(\mathstrut +\mathstrut 107q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.b.a \(1\) \(0.518\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(-5\) \(q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots\)
19.3.b.b \(2\) \(0.518\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(8\) \(-10\) \(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)