# Properties

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

## 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

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