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Properties

Label 106.2
Level 106
Weight 2
Dimension 116
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 1404
Trace bound 4

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Defining parameters

Level: \( N \) = \( 106 = 2 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1404\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(106))\).

Total New Old
Modular forms 403 116 287
Cusp forms 300 116 184
Eisenstein series 103 0 103

Trace form

\( 116 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 116 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} + 7 q^{40} + 10 q^{41} + 72 q^{42} + 60 q^{43} - 12 q^{44} + 182 q^{45} + 28 q^{46} + 4 q^{47} + 48 q^{48} + 47 q^{49} + 86 q^{50} + 136 q^{51} + 38 q^{52} + 103 q^{53} + 116 q^{54} + 84 q^{55} + 44 q^{56} + 128 q^{57} + 87 q^{58} + 44 q^{59} + 28 q^{60} - 10 q^{61} + 20 q^{62} + 156 q^{63} - q^{64} + 20 q^{65} + 56 q^{66} - 16 q^{67} - 5 q^{68} - 96 q^{69} - 48 q^{70} - 72 q^{71} - 13 q^{72} - 74 q^{73} - 38 q^{74} - 124 q^{75} - 20 q^{76} - 96 q^{77} - 56 q^{78} - 80 q^{79} - 6 q^{80} - 121 q^{81} - 42 q^{82} - 84 q^{83} - 32 q^{84} - 108 q^{85} - 44 q^{86} - 68 q^{87} - 12 q^{88} - 25 q^{89} - 78 q^{90} - 8 q^{91} - 24 q^{92} - 24 q^{93} - 48 q^{94} - 16 q^{95} - 4 q^{96} + 123 q^{97} - 57 q^{98} + 104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)

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
106.2.a \(\chi_{106}(1, \cdot)\) 106.2.a.a 1 1
106.2.a.b 1
106.2.a.c 1
106.2.a.d 1
106.2.b \(\chi_{106}(105, \cdot)\) 106.2.b.a 2 1
106.2.b.b 2
106.2.d \(\chi_{106}(13, \cdot)\) 106.2.d.a 24 12
106.2.d.b 36
106.2.e \(\chi_{106}(7, \cdot)\) 106.2.e.a 48 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(106)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)