# Properties

 Label 228.2 Level 228 Weight 2 Dimension 594 Nonzero newspaces 12 Newform subspaces 24 Sturm bound 5760 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$228 = 2^{2} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$24$$ Sturm bound: $$5760$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(228))$$.

Total New Old
Modular forms 1620 658 962
Cusp forms 1261 594 667
Eisenstein series 359 64 295

## Trace form

 $$594q - 18q^{4} - 9q^{6} - 18q^{9} + O(q^{10})$$ $$594q - 18q^{4} - 9q^{6} - 18q^{9} - 18q^{10} - 9q^{12} - 12q^{13} + 18q^{15} - 18q^{16} + 18q^{17} - 18q^{18} + 42q^{19} + 3q^{21} - 18q^{22} + 18q^{23} - 9q^{24} - 6q^{27} - 72q^{28} - 36q^{29} - 72q^{30} - 36q^{31} - 90q^{32} - 72q^{33} - 108q^{34} - 72q^{35} - 99q^{36} - 108q^{37} - 126q^{38} - 54q^{39} - 144q^{40} - 36q^{41} - 99q^{42} - 72q^{43} - 90q^{44} - 99q^{45} - 108q^{46} - 36q^{47} - 72q^{48} - 72q^{49} - 54q^{50} - 54q^{51} - 18q^{52} - 9q^{54} - 63q^{57} - 36q^{58} - 18q^{60} - 120q^{61} + 90q^{62} - 42q^{63} + 126q^{64} - 108q^{65} + 63q^{66} - 72q^{67} + 126q^{68} - 189q^{69} + 198q^{70} - 36q^{71} + 45q^{72} - 198q^{73} + 144q^{74} - 42q^{75} + 162q^{76} - 234q^{77} + 63q^{78} - 48q^{79} + 144q^{80} + 18q^{81} + 252q^{82} + 18q^{83} + 99q^{84} - 252q^{85} + 126q^{86} + 36q^{87} + 126q^{88} - 54q^{89} + 54q^{90} + 24q^{91} + 90q^{92} + 12q^{93} + 54q^{95} + 54q^{96} + 18q^{97} + 135q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$

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
228.2.a $$\chi_{228}(1, \cdot)$$ 228.2.a.a 1 1
228.2.a.b 1
228.2.a.c 2
228.2.c $$\chi_{228}(191, \cdot)$$ 228.2.c.a 36 1
228.2.d $$\chi_{228}(113, \cdot)$$ 228.2.d.a 2 1
228.2.d.b 4
228.2.f $$\chi_{228}(151, \cdot)$$ 228.2.f.a 10 1
228.2.f.b 10
228.2.i $$\chi_{228}(49, \cdot)$$ 228.2.i.a 4 2
228.2.i.b 4
228.2.k $$\chi_{228}(31, \cdot)$$ 228.2.k.a 20 2
228.2.k.b 20
228.2.m $$\chi_{228}(11, \cdot)$$ 228.2.m.a 72 2
228.2.p $$\chi_{228}(65, \cdot)$$ 228.2.p.a 2 2
228.2.p.b 2
228.2.p.c 4
228.2.p.d 4
228.2.q $$\chi_{228}(25, \cdot)$$ 228.2.q.a 6 6
228.2.q.b 12
228.2.t $$\chi_{228}(29, \cdot)$$ 228.2.t.a 6 6
228.2.t.b 36
228.2.v $$\chi_{228}(23, \cdot)$$ 228.2.v.a 216 6
228.2.w $$\chi_{228}(67, \cdot)$$ 228.2.w.a 60 6
228.2.w.b 60

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(228))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(228)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 2}$$