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Properties

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

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Defining parameters

Level: \( N \) = \( 109 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 12 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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