Properties

Label 189.2
Level 189
Weight 2
Dimension 902
Nonzero newspaces 16
Newforms 37
Sturm bound 5184
Trace bound 9

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Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newforms: \( 37 \)
Sturm bound: \(5184\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(189))\).

Total New Old
Modular forms 1476 1062 414
Cusp forms 1117 902 215
Eisenstein series 359 160 199

Trace form

\(902q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut -\mathstrut 24q^{3} \) \(\mathstrut -\mathstrut 26q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 36q^{6} \) \(\mathstrut -\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 60q^{8} \) \(\mathstrut -\mathstrut 36q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(902q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut -\mathstrut 24q^{3} \) \(\mathstrut -\mathstrut 26q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 36q^{6} \) \(\mathstrut -\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 60q^{8} \) \(\mathstrut -\mathstrut 36q^{9} \) \(\mathstrut -\mathstrut 36q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 60q^{12} \) \(\mathstrut -\mathstrut 42q^{13} \) \(\mathstrut -\mathstrut 51q^{14} \) \(\mathstrut -\mathstrut 90q^{15} \) \(\mathstrut -\mathstrut 70q^{16} \) \(\mathstrut -\mathstrut 60q^{17} \) \(\mathstrut -\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 60q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 114q^{22} \) \(\mathstrut -\mathstrut 18q^{23} \) \(\mathstrut -\mathstrut 52q^{25} \) \(\mathstrut -\mathstrut 18q^{27} \) \(\mathstrut -\mathstrut 106q^{28} \) \(\mathstrut -\mathstrut 48q^{29} \) \(\mathstrut -\mathstrut 18q^{30} \) \(\mathstrut -\mathstrut 54q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 36q^{33} \) \(\mathstrut -\mathstrut 96q^{34} \) \(\mathstrut -\mathstrut 72q^{35} \) \(\mathstrut -\mathstrut 108q^{36} \) \(\mathstrut -\mathstrut 82q^{37} \) \(\mathstrut -\mathstrut 168q^{38} \) \(\mathstrut -\mathstrut 102q^{39} \) \(\mathstrut -\mathstrut 120q^{40} \) \(\mathstrut -\mathstrut 108q^{41} \) \(\mathstrut -\mathstrut 54q^{42} \) \(\mathstrut -\mathstrut 130q^{43} \) \(\mathstrut -\mathstrut 108q^{44} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 96q^{46} \) \(\mathstrut -\mathstrut 30q^{47} \) \(\mathstrut +\mathstrut 102q^{48} \) \(\mathstrut -\mathstrut 43q^{49} \) \(\mathstrut +\mathstrut 78q^{50} \) \(\mathstrut +\mathstrut 54q^{51} \) \(\mathstrut +\mathstrut 12q^{52} \) \(\mathstrut +\mathstrut 138q^{53} \) \(\mathstrut +\mathstrut 180q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 267q^{56} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut +\mathstrut 150q^{59} \) \(\mathstrut +\mathstrut 180q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 270q^{62} \) \(\mathstrut +\mathstrut 81q^{63} \) \(\mathstrut +\mathstrut 100q^{64} \) \(\mathstrut +\mathstrut 150q^{65} \) \(\mathstrut +\mathstrut 126q^{66} \) \(\mathstrut +\mathstrut 28q^{67} \) \(\mathstrut +\mathstrut 276q^{68} \) \(\mathstrut +\mathstrut 36q^{69} \) \(\mathstrut +\mathstrut 57q^{70} \) \(\mathstrut -\mathstrut 30q^{71} \) \(\mathstrut +\mathstrut 108q^{72} \) \(\mathstrut +\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 21q^{77} \) \(\mathstrut -\mathstrut 36q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 108q^{81} \) \(\mathstrut -\mathstrut 120q^{82} \) \(\mathstrut -\mathstrut 180q^{83} \) \(\mathstrut -\mathstrut 42q^{84} \) \(\mathstrut -\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 258q^{86} \) \(\mathstrut -\mathstrut 54q^{87} \) \(\mathstrut -\mathstrut 42q^{88} \) \(\mathstrut -\mathstrut 156q^{89} \) \(\mathstrut -\mathstrut 72q^{90} \) \(\mathstrut -\mathstrut 123q^{91} \) \(\mathstrut -\mathstrut 126q^{92} \) \(\mathstrut +\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 132q^{94} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 36q^{96} \) \(\mathstrut -\mathstrut 90q^{97} \) \(\mathstrut -\mathstrut 96q^{98} \) \(\mathstrut -\mathstrut 18q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)

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
189.2.a \(\chi_{189}(1, \cdot)\) 189.2.a.a 1 1
189.2.a.b 1
189.2.a.c 1
189.2.a.d 1
189.2.a.e 2
189.2.a.f 2
189.2.c \(\chi_{189}(188, \cdot)\) 189.2.c.a 2 1
189.2.c.b 4
189.2.c.c 4
189.2.e \(\chi_{189}(109, \cdot)\) 189.2.e.a 2 2
189.2.e.b 2
189.2.e.c 2
189.2.e.d 4
189.2.e.e 6
189.2.e.f 6
189.2.f \(\chi_{189}(64, \cdot)\) 189.2.f.a 6 2
189.2.f.b 6
189.2.g \(\chi_{189}(100, \cdot)\) 189.2.g.a 2 2
189.2.g.b 10
189.2.h \(\chi_{189}(37, \cdot)\) 189.2.h.a 2 2
189.2.h.b 10
189.2.i \(\chi_{189}(143, \cdot)\) 189.2.i.a 2 2
189.2.i.b 10
189.2.o \(\chi_{189}(62, \cdot)\) 189.2.o.a 12 2
189.2.p \(\chi_{189}(26, \cdot)\) 189.2.p.a 2 2
189.2.p.b 4
189.2.p.c 4
189.2.p.d 12
189.2.s \(\chi_{189}(17, \cdot)\) 189.2.s.a 2 2
189.2.s.b 10
189.2.u \(\chi_{189}(4, \cdot)\) 189.2.u.a 132 6
189.2.v \(\chi_{189}(22, \cdot)\) 189.2.v.a 54 6
189.2.v.b 54
189.2.w \(\chi_{189}(25, \cdot)\) 189.2.w.a 132 6
189.2.ba \(\chi_{189}(5, \cdot)\) 189.2.ba.a 132 6
189.2.bd \(\chi_{189}(47, \cdot)\) 189.2.bd.a 132 6
189.2.be \(\chi_{189}(20, \cdot)\) 189.2.be.a 132 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(189))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(189)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)