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Properties

Label 19.2.e
Level $19$
Weight $2$
Character orbit 19.e
Rep. character $\chi_{19}(4,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $6$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(19, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

Trace form

\( 6q - 6q^{2} - 3q^{3} - 6q^{5} + 3q^{6} + 6q^{8} + 3q^{9} + O(q^{10}) \) \( 6q - 6q^{2} - 3q^{3} - 6q^{5} + 3q^{6} + 6q^{8} + 3q^{9} + 9q^{10} + 3q^{12} - 3q^{13} - 3q^{14} + 3q^{15} - 18q^{16} + 3q^{17} - 6q^{18} - 12q^{19} - 6q^{20} + 6q^{23} + 15q^{24} + 15q^{26} + 6q^{27} + 6q^{28} - 3q^{29} + 9q^{31} + 9q^{32} - 9q^{33} + 6q^{35} - 24q^{36} - 15q^{38} - 24q^{39} + 21q^{41} - 3q^{42} - 3q^{43} + 9q^{44} - 15q^{45} - 18q^{46} - 3q^{47} - 3q^{48} + 15q^{49} - 15q^{50} + 3q^{51} + 15q^{52} - 3q^{53} + 30q^{54} + 18q^{55} - 6q^{56} + 24q^{57} + 36q^{58} + 12q^{59} - 6q^{60} - 12q^{61} - 12q^{62} + 12q^{63} - 12q^{64} - 12q^{65} - 9q^{66} - 30q^{67} - 15q^{68} - 12q^{69} - 9q^{70} - 6q^{71} - 12q^{72} - 12q^{73} + 15q^{74} + 30q^{75} + 36q^{76} - 18q^{77} + 15q^{78} - 39q^{79} + 3q^{80} + 6q^{81} - 54q^{82} + 3q^{84} + 24q^{86} - 21q^{87} + 9q^{88} - 12q^{89} + 18q^{90} + 15q^{91} + 42q^{92} + 9q^{93} + 18q^{94} + 39q^{95} + 18q^{96} + 18q^{97} - 9q^{98} + 9q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.2.e.a \(6\) \(0.152\) \(\Q(\zeta_{18})\) None \(-6\) \(-3\) \(-6\) \(0\) \(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)