Properties

Label 109.2
Level 109
Weight 2
Dimension 442
Nonzero newspaces 8
Newforms 12
Sturm bound 1980
Trace bound 2

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Defining parameters

Level: \( N \) = \( 109 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newforms: \( 12 \)
Sturm bound: \(1980\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(109))\).

Total New Old
Modular forms 549 549 0
Cusp forms 442 442 0
Eisenstein series 107 107 0

Trace form

\(442q \) \(\mathstrut -\mathstrut 51q^{2} \) \(\mathstrut -\mathstrut 50q^{3} \) \(\mathstrut -\mathstrut 47q^{4} \) \(\mathstrut -\mathstrut 48q^{5} \) \(\mathstrut -\mathstrut 42q^{6} \) \(\mathstrut -\mathstrut 46q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 41q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(442q \) \(\mathstrut -\mathstrut 51q^{2} \) \(\mathstrut -\mathstrut 50q^{3} \) \(\mathstrut -\mathstrut 47q^{4} \) \(\mathstrut -\mathstrut 48q^{5} \) \(\mathstrut -\mathstrut 42q^{6} \) \(\mathstrut -\mathstrut 46q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 41q^{9} \) \(\mathstrut -\mathstrut 36q^{10} \) \(\mathstrut -\mathstrut 42q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 40q^{13} \) \(\mathstrut -\mathstrut 30q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut -\mathstrut 23q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 15q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 22q^{21} \) \(\mathstrut -\mathstrut 18q^{22} \) \(\mathstrut -\mathstrut 30q^{23} \) \(\mathstrut +\mathstrut 6q^{24} \) \(\mathstrut -\mathstrut 23q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 14q^{27} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 18q^{30} \) \(\mathstrut -\mathstrut 22q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 37q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 36q^{40} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut +\mathstrut 42q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 30q^{44} \) \(\mathstrut +\mathstrut 24q^{45} \) \(\mathstrut +\mathstrut 18q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 70q^{48} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 39q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 44q^{52} \) \(\mathstrut +\mathstrut 66q^{54} \) \(\mathstrut +\mathstrut 18q^{55} \) \(\mathstrut +\mathstrut 66q^{56} \) \(\mathstrut +\mathstrut 26q^{57} \) \(\mathstrut +\mathstrut 36q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut +\mathstrut 114q^{60} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut 42q^{62} \) \(\mathstrut +\mathstrut 50q^{63} \) \(\mathstrut +\mathstrut 73q^{64} \) \(\mathstrut +\mathstrut 30q^{65} \) \(\mathstrut +\mathstrut 90q^{66} \) \(\mathstrut +\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 72q^{68} \) \(\mathstrut +\mathstrut 42q^{69} \) \(\mathstrut +\mathstrut 90q^{70} \) \(\mathstrut +\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 141q^{72} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 60q^{74} \) \(\mathstrut +\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 86q^{76} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 114q^{78} \) \(\mathstrut +\mathstrut 26q^{79} \) \(\mathstrut +\mathstrut 132q^{80} \) \(\mathstrut +\mathstrut 67q^{81} \) \(\mathstrut +\mathstrut 72q^{82} \) \(\mathstrut +\mathstrut 30q^{83} \) \(\mathstrut +\mathstrut 170q^{84} \) \(\mathstrut +\mathstrut 54q^{85} \) \(\mathstrut +\mathstrut 78q^{86} \) \(\mathstrut +\mathstrut 66q^{87} \) \(\mathstrut +\mathstrut 126q^{88} \) \(\mathstrut +\mathstrut 36q^{89} \) \(\mathstrut +\mathstrut 45q^{90} \) \(\mathstrut -\mathstrut 68q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 234q^{94} \) \(\mathstrut -\mathstrut 96q^{95} \) \(\mathstrut -\mathstrut 234q^{96} \) \(\mathstrut -\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 99q^{98} \) \(\mathstrut -\mathstrut 222q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(109))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
109.2.a \(\chi_{109}(1, \cdot)\) 109.2.a.a 1 1
109.2.a.b 3
109.2.a.c 4
109.2.b \(\chi_{109}(108, \cdot)\) 109.2.b.a 2 1
109.2.b.b 6
109.2.c \(\chi_{109}(45, \cdot)\) 109.2.c.a 14 2
109.2.e \(\chi_{109}(46, \cdot)\) 109.2.e.a 2 2
109.2.e.b 14
109.2.f \(\chi_{109}(16, \cdot)\) 109.2.f.a 42 6
109.2.h \(\chi_{109}(4, \cdot)\) 109.2.h.a 48 6
109.2.i \(\chi_{109}(3, \cdot)\) 109.2.i.a 144 18
109.2.k \(\chi_{109}(12, \cdot)\) 109.2.k.a 162 18