Properties

Label 206.2
Level 206
Weight 2
Dimension 441
Nonzero newspaces 4
Newform subspaces 12
Sturm bound 5304
Trace bound 1

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Defining parameters

Level: \( N \) = \( 206 = 2 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 12 \)
Sturm bound: \(5304\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(206))\).

Total New Old
Modular forms 1428 441 987
Cusp forms 1225 441 784
Eisenstein series 203 0 203

Trace form

\( 441 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 441 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} - 6 q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 78 q^{45} - 24 q^{46} - 48 q^{47} - 4 q^{48} - 57 q^{49} - 31 q^{50} - 72 q^{51} - 14 q^{52} - 54 q^{53} - 40 q^{54} - 72 q^{55} - 8 q^{56} - 80 q^{57} - 30 q^{58} - 60 q^{59} - 24 q^{60} - 62 q^{61} - 32 q^{62} - 104 q^{63} - q^{64} - 84 q^{65} - 48 q^{66} - 68 q^{67} - 18 q^{68} - 96 q^{69} - 48 q^{70} - 72 q^{71} - 13 q^{72} - 74 q^{73} - 38 q^{74} - 124 q^{75} - 20 q^{76} - 96 q^{77} - 56 q^{78} - 80 q^{79} - 6 q^{80} - 121 q^{81} - 42 q^{82} - 84 q^{83} + 2 q^{84} + 96 q^{85} + 58 q^{86} + 84 q^{87} - 12 q^{88} + 114 q^{89} + 330 q^{90} + 330 q^{91} + 78 q^{92} + 280 q^{93} + 156 q^{94} + 186 q^{95} - 4 q^{96} + 344 q^{97} + 351 q^{98} + 354 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(206))\)

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
206.2.a \(\chi_{206}(1, \cdot)\) 206.2.a.a 1 1
206.2.a.b 2
206.2.a.c 2
206.2.a.d 4
206.2.c \(\chi_{206}(149, \cdot)\) 206.2.c.a 2 2
206.2.c.b 6
206.2.c.c 8
206.2.e \(\chi_{206}(9, \cdot)\) 206.2.e.a 16 16
206.2.e.b 64
206.2.e.c 80
206.2.g \(\chi_{206}(7, \cdot)\) 206.2.g.a 128 32
206.2.g.b 128

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(206))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(206)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 2}\)