Properties

Label 19.5.b
Level $19$
Weight $5$
Character orbit 19.b
Rep. character $\chi_{19}(18,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $8$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(19, [\chi])\).

Total New Old
Modular forms 7 7 0
Cusp forms 5 5 0
Eisenstein series 2 2 0

Trace form

\( 5q + 10q^{4} - 11q^{5} + 26q^{6} + 63q^{7} - 197q^{9} + O(q^{10}) \) \( 5q + 10q^{4} - 11q^{5} + 26q^{6} + 63q^{7} - 197q^{9} - 11q^{11} - 198q^{16} - 53q^{17} + 475q^{19} + 340q^{20} - 236q^{23} + 1910q^{24} - 1650q^{25} + 414q^{26} - 58q^{28} - 784q^{30} - 4129q^{35} - 5076q^{36} + 2166q^{38} + 6362q^{39} + 3950q^{42} + 6513q^{43} - 7784q^{44} + 7693q^{45} - 6371q^{47} + 576q^{49} - 15542q^{54} - 8313q^{55} + 10450q^{57} + 14638q^{58} + 3325q^{61} + 18396q^{62} - 28943q^{63} + 7590q^{64} - 7244q^{66} - 842q^{68} - 25201q^{73} - 17868q^{74} + 18088q^{76} + 17111q^{77} + 9856q^{80} + 47273q^{81} - 29164q^{82} + 27598q^{83} - 15845q^{85} - 7214q^{87} - 27158q^{92} - 40004q^{93} + 5833q^{95} + 47538q^{96} + 4169q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.5.b.a \(1\) \(1.964\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(31\) \(-73\) \(q+2^{4}q^{4}+31q^{5}-73q^{7}+3^{4}q^{9}+\cdots\)
19.5.b.b \(4\) \(1.964\) 4.0.12107488.1 None \(0\) \(0\) \(-42\) \(136\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-3+3\beta _{2})q^{4}+\cdots\)