↑

Properties

Label 201.2
Level 201
Weight 2
Dimension 1055
Nonzero newspaces 8
Newform subspaces 18
Sturm bound 5984
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 201 = 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 18 \)
Sturm bound: \(5984\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(201))\).

Total New Old
Modular forms 1628 1187 441
Cusp forms 1365 1055 310
Eisenstein series 263 132 131

Trace form

\( 1055 q - 3 q^{2} - 34 q^{3} - 73 q^{4} - 6 q^{5} - 36 q^{6} - 74 q^{7} - 15 q^{8} - 34 q^{9} + O(q^{10}) \) \( 1055 q - 3 q^{2} - 34 q^{3} - 73 q^{4} - 6 q^{5} - 36 q^{6} - 74 q^{7} - 15 q^{8} - 34 q^{9} - 84 q^{10} - 12 q^{11} - 40 q^{12} - 80 q^{13} - 24 q^{14} - 39 q^{15} - 97 q^{16} - 18 q^{17} - 36 q^{18} - 86 q^{19} - 42 q^{20} - 41 q^{21} - 102 q^{22} - 24 q^{23} - 48 q^{24} - 97 q^{25} - 42 q^{26} - 34 q^{27} - 122 q^{28} - 30 q^{29} - 51 q^{30} - 98 q^{31} - 63 q^{32} - 45 q^{33} - 120 q^{34} - 48 q^{35} - 40 q^{36} - 104 q^{37} - 60 q^{38} - 47 q^{39} - 156 q^{40} - 42 q^{41} - 57 q^{42} - 110 q^{43} - 84 q^{44} - 39 q^{45} - 138 q^{46} - 48 q^{47} - 64 q^{48} - 123 q^{49} - 93 q^{50} - 51 q^{51} - 76 q^{52} + 12 q^{53} - 36 q^{54} + 60 q^{55} + 276 q^{56} + 24 q^{57} + 108 q^{58} + 72 q^{59} + 189 q^{60} + 136 q^{61} + 36 q^{62} - 30 q^{63} + 467 q^{64} + 180 q^{65} + 228 q^{66} - q^{67} + 138 q^{68} + 9 q^{69} + 318 q^{70} + 192 q^{71} + 84 q^{72} + 146 q^{73} + 18 q^{74} + 68 q^{75} + 322 q^{76} + 36 q^{77} + 57 q^{78} + 8 q^{79} + 210 q^{80} - 34 q^{81} + 6 q^{82} - 18 q^{83} - 45 q^{84} - 174 q^{85} - 132 q^{86} - 63 q^{87} - 246 q^{88} - 90 q^{89} - 51 q^{90} - 178 q^{91} - 168 q^{92} - 65 q^{93} - 210 q^{94} - 120 q^{95} - 96 q^{96} - 164 q^{97} - 171 q^{98} - 45 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)

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
201.2.a \(\chi_{201}(1, \cdot)\) 201.2.a.a 1 1
201.2.a.b 1
201.2.a.c 1
201.2.a.d 3
201.2.a.e 5
201.2.d \(\chi_{201}(200, \cdot)\) 201.2.d.a 20 1
201.2.e \(\chi_{201}(37, \cdot)\) 201.2.e.a 2 2
201.2.e.b 10
201.2.e.c 10
201.2.f \(\chi_{201}(38, \cdot)\) 201.2.f.a 2 2
201.2.f.b 40
201.2.i \(\chi_{201}(22, \cdot)\) 201.2.i.a 50 10
201.2.i.b 70
201.2.j \(\chi_{201}(5, \cdot)\) 201.2.j.a 200 10
201.2.m \(\chi_{201}(4, \cdot)\) 201.2.m.a 100 20
201.2.m.b 120
201.2.p \(\chi_{201}(2, \cdot)\) 201.2.p.a 20 20
201.2.p.b 400

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(201))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(201)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 2}\)