Properties

Label 109.2.h
Level 109
Weight 2
Character orbit h
Rep. character \(\chi_{109}(4,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 48
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 109.h (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 109 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
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 60 60 0
Cusp forms 48 48 0
Eisenstein series 12 12 0

Trace form

\( 48q - 9q^{2} - 6q^{3} + 15q^{4} - 6q^{5} + 3q^{7} + 12q^{9} + O(q^{10}) \) \( 48q - 9q^{2} - 6q^{3} + 15q^{4} - 6q^{5} + 3q^{7} + 12q^{9} - 9q^{10} + 9q^{11} - 3q^{12} - 15q^{14} - 12q^{15} - 3q^{16} - 9q^{17} - 69q^{18} - 9q^{19} - 42q^{20} + 15q^{21} + 12q^{22} - 18q^{23} + 60q^{24} - 18q^{25} - 12q^{26} - 45q^{27} - 54q^{28} + 33q^{29} - 33q^{30} - 18q^{31} + 9q^{32} + 3q^{34} + 18q^{35} + 105q^{36} + 15q^{37} - 33q^{38} - 6q^{39} - 12q^{40} - 36q^{42} + 9q^{43} + 66q^{44} - 6q^{45} - 60q^{46} - 6q^{47} + 57q^{48} + 39q^{49} + 87q^{50} - 48q^{51} - 36q^{52} + 15q^{53} + 90q^{54} - 9q^{55} + 3q^{56} + 15q^{57} - 27q^{58} - 6q^{59} - 33q^{60} + 78q^{61} + 36q^{62} + 72q^{63} + 126q^{64} - 54q^{65} + 9q^{66} + 54q^{67} - 3q^{69} + 39q^{70} + 15q^{71} - 99q^{72} - 21q^{73} + 24q^{74} - 30q^{75} + 81q^{77} + 27q^{78} - 126q^{79} + 45q^{80} - 75q^{81} - 3q^{82} - 21q^{83} - 63q^{84} - 6q^{85} - 189q^{86} + 114q^{87} + 12q^{88} + 3q^{89} + 225q^{90} - 72q^{91} - 27q^{92} + 33q^{93} - 42q^{94} - 39q^{95} - 99q^{96} + 51q^{97} - 150q^{98} - 93q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(109, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
109.2.h.a \(48\) \(0.870\) None \(-9\) \(-6\) \(-6\) \(3\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database