Properties

Label 109.2.f
Level 109
Weight 2
Character orbit f
Rep. character \(\chi_{109}(16,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 42
Newforms 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 109.f (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 109 \)
Character field: \(\Q(\zeta_{9})\)
Newforms: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(109, [\chi])\).

Total New Old
Modular forms 54 54 0
Cusp forms 42 42 0
Eisenstein series 12 12 0

Trace form

\(42q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(42q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut -\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 30q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 30q^{20} \) \(\mathstrut -\mathstrut 3q^{21} \) \(\mathstrut -\mathstrut 18q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 15q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 21q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 21q^{36} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut +\mathstrut 27q^{38} \) \(\mathstrut +\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 24q^{40} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 36q^{44} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 42q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut +\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 36q^{54} \) \(\mathstrut +\mathstrut 21q^{55} \) \(\mathstrut +\mathstrut 57q^{56} \) \(\mathstrut -\mathstrut 15q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut +\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 33q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 78q^{62} \) \(\mathstrut -\mathstrut 48q^{63} \) \(\mathstrut -\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut -\mathstrut 15q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 15q^{69} \) \(\mathstrut +\mathstrut 39q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 66q^{73} \) \(\mathstrut -\mathstrut 24q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 3q^{78} \) \(\mathstrut +\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 15q^{81} \) \(\mathstrut +\mathstrut 21q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 87q^{84} \) \(\mathstrut +\mathstrut 120q^{85} \) \(\mathstrut -\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 48q^{88} \) \(\mathstrut +\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 24q^{90} \) \(\mathstrut +\mathstrut 63q^{92} \) \(\mathstrut -\mathstrut 75q^{93} \) \(\mathstrut -\mathstrut 30q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut -\mathstrut 21q^{96} \) \(\mathstrut +\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 126q^{98} \) \(\mathstrut +\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(109, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
109.2.f.a \(42\) \(0.870\) None \(0\) \(-6\) \(-6\) \(3\)