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Properties

Label 109.3
Level 109
Weight 3
Dimension 936
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 2970
Trace bound 1

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Defining parameters

Level: \( N \) = \( 109 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(2970\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(109))\).

Total New Old
Modular forms 1044 1044 0
Cusp forms 936 936 0
Eisenstein series 108 108 0

Trace form

\( 936 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} + O(q^{10}) \) \( 936 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18} - 54 q^{19} - 54 q^{20} - 54 q^{21} - 54 q^{22} - 54 q^{23} - 54 q^{24} - 54 q^{25} - 54 q^{26} - 54 q^{27} - 54 q^{28} - 54 q^{29} - 54 q^{30} - 54 q^{31} - 54 q^{32} - 54 q^{33} - 54 q^{34} - 54 q^{35} - 54 q^{36} - 54 q^{37} - 54 q^{38} - 54 q^{39} - 54 q^{40} - 54 q^{41} - 54 q^{42} - 54 q^{43} - 54 q^{44} - 54 q^{45} - 54 q^{46} - 54 q^{47} - 54 q^{48} - 54 q^{49} - 54 q^{50} - 54 q^{51} - 54 q^{52} - 54 q^{53} - 54 q^{54} - 54 q^{55} - 54 q^{56} - 54 q^{57} - 54 q^{58} - 54 q^{59} - 54 q^{60} - 54 q^{61} - 54 q^{62} - 54 q^{63} - 54 q^{64} - 54 q^{65} - 54 q^{66} - 54 q^{67} - 54 q^{68} - 54 q^{69} - 54 q^{70} - 54 q^{71} - 54 q^{72} - 54 q^{73} - 54 q^{74} - 54 q^{75} - 54 q^{76} - 54 q^{77} - 54 q^{78} - 54 q^{79} - 54 q^{80} - 54 q^{81} - 54 q^{82} - 54 q^{83} - 54 q^{84} - 54 q^{85} - 54 q^{86} - 54 q^{87} - 54 q^{88} - 54 q^{89} + 2376 q^{90} + 2088 q^{91} + 3402 q^{92} + 1836 q^{93} + 4482 q^{94} + 2052 q^{95} + 5130 q^{96} + 1134 q^{97} + 2106 q^{98} + 2862 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(109))\)

We only show spaces with odd 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
109.3.d \(\chi_{109}(33, \cdot)\) 109.3.d.a 36 2
109.3.g \(\chi_{109}(8, \cdot)\) 109.3.g.a 72 4
109.3.j \(\chi_{109}(2, \cdot)\) 109.3.j.a 216 12
109.3.l \(\chi_{109}(6, \cdot)\) 109.3.l.a 612 36