Properties

Label 19.3.b
Level $19$
Weight $3$
Character orbit 19.b
Rep. character $\chi_{19}(18,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

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 \(0\) \(0\) \(8\) \(-10\) \(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)