# Properties

 Label 222.2 Level 222 Weight 2 Dimension 343 Nonzero newspaces 9 Newform subspaces 22 Sturm bound 5472 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$222 = 2 \cdot 3 \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$9$$ Newform subspaces: $$22$$ Sturm bound: $$5472$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(222))$$.

Total New Old
Modular forms 1512 343 1169
Cusp forms 1225 343 882
Eisenstein series 287 0 287

## Trace form

 $$343 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$343 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} - 4 q^{26} - 11 q^{27} - 16 q^{28} - 42 q^{29} - 66 q^{30} - 184 q^{31} + q^{32} - 60 q^{33} - 126 q^{34} - 168 q^{35} - 17 q^{36} - 131 q^{37} - 52 q^{38} - 70 q^{39} - 84 q^{40} - 174 q^{41} - 64 q^{42} - 100 q^{43} + 12 q^{44} + 6 q^{45} - 120 q^{46} - 24 q^{47} - 11 q^{48} - 39 q^{49} + 13 q^{50} + 18 q^{51} + 14 q^{52} + 54 q^{53} + q^{54} + 72 q^{55} + 8 q^{56} + 20 q^{57} + 30 q^{58} - 12 q^{59} + 6 q^{60} - 28 q^{61} + 32 q^{62} - 100 q^{63} + q^{64} - 78 q^{65} + 12 q^{66} - 4 q^{67} + 18 q^{68} - 120 q^{69} + 48 q^{70} - 72 q^{71} + q^{72} - 70 q^{73} + 37 q^{74} - 149 q^{75} + 20 q^{76} - 48 q^{77} + 14 q^{78} - 64 q^{79} + 6 q^{80} - 143 q^{81} + 42 q^{82} + 12 q^{83} + 8 q^{84} - 54 q^{85} + 44 q^{86} - 78 q^{87} + 12 q^{88} + 6 q^{90} + 40 q^{91} + 24 q^{92} + 140 q^{93} + 48 q^{94} + 120 q^{95} + q^{96} + 98 q^{97} + 57 q^{98} + 192 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(222))$$

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
222.2.a $$\chi_{222}(1, \cdot)$$ 222.2.a.a 1 1
222.2.a.b 1
222.2.a.c 1
222.2.a.d 1
222.2.a.e 1
222.2.c $$\chi_{222}(73, \cdot)$$ 222.2.c.a 2 1
222.2.c.b 4
222.2.e $$\chi_{222}(121, \cdot)$$ 222.2.e.a 2 2
222.2.e.b 2
222.2.e.c 4
222.2.g $$\chi_{222}(179, \cdot)$$ 222.2.g.a 28 2
222.2.j $$\chi_{222}(85, \cdot)$$ 222.2.j.a 4 2
222.2.j.b 8
222.2.k $$\chi_{222}(7, \cdot)$$ 222.2.k.a 6 6
222.2.k.b 6
222.2.k.c 6
222.2.k.d 6
222.2.k.e 12
222.2.m $$\chi_{222}(23, \cdot)$$ 222.2.m.a 56 4
222.2.n $$\chi_{222}(25, \cdot)$$ 222.2.n.a 24 6
222.2.n.b 24
222.2.q $$\chi_{222}(5, \cdot)$$ 222.2.q.a 144 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(222))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(222)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(111))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(222))$$$$^{\oplus 1}$$