# Properties

 Label 228.3 Level 228 Weight 3 Dimension 1218 Nonzero newspaces 12 Newform subspaces 27 Sturm bound 8640 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$228 = 2^{2} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$12$$ Newform subspaces: $$27$$ Sturm bound: $$8640$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(228))$$.

Total New Old
Modular forms 3060 1290 1770
Cusp forms 2700 1218 1482
Eisenstein series 360 72 288

## Trace form

 $$1218 q + 4 q^{2} + 6 q^{3} - 10 q^{4} + 8 q^{5} - 21 q^{6} - 4 q^{7} - 32 q^{8} - 24 q^{9} + O(q^{10})$$ $$1218 q + 4 q^{2} + 6 q^{3} - 10 q^{4} + 8 q^{5} - 21 q^{6} - 4 q^{7} - 32 q^{8} - 24 q^{9} - 26 q^{10} + 15 q^{12} - 120 q^{13} + 48 q^{14} - 54 q^{15} + 14 q^{16} - 58 q^{17} - 12 q^{18} + 16 q^{19} - 16 q^{20} + 9 q^{21} - 66 q^{22} + 90 q^{23} - 9 q^{24} + 250 q^{25} + 8 q^{26} + 171 q^{27} + 372 q^{28} + 392 q^{29} + 456 q^{30} + 308 q^{31} + 514 q^{32} + 246 q^{33} + 292 q^{34} + 144 q^{35} + 57 q^{36} - 156 q^{37} - 198 q^{38} - 240 q^{39} - 332 q^{40} - 376 q^{41} - 411 q^{42} - 388 q^{43} - 534 q^{44} - 177 q^{45} - 636 q^{46} - 360 q^{47} - 798 q^{48} - 382 q^{49} - 786 q^{50} + 99 q^{51} - 2 q^{52} + 296 q^{53} + 27 q^{54} + 87 q^{57} - 140 q^{58} - 408 q^{60} + 888 q^{61} - 1218 q^{62} - 216 q^{63} - 1858 q^{64} + 1096 q^{65} - 705 q^{66} + 332 q^{67} - 802 q^{68} + 303 q^{69} - 1194 q^{70} + 144 q^{71} - 75 q^{72} + 564 q^{73} - 40 q^{74} + 150 q^{75} + 306 q^{76} - 1002 q^{77} + 201 q^{78} - 592 q^{79} + 656 q^{80} - 684 q^{81} + 2104 q^{82} - 882 q^{83} + 1059 q^{84} - 3484 q^{85} + 1722 q^{86} - 936 q^{87} + 1854 q^{88} - 2110 q^{89} + 60 q^{90} - 896 q^{91} + 1146 q^{92} - 1074 q^{93} + 204 q^{94} + 54 q^{95} - 1050 q^{96} + 114 q^{97} + 4 q^{98} - 522 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(228))$$

We only show spaces with odd 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
228.3.b $$\chi_{228}(227, \cdot)$$ 228.3.b.a 1 1
228.3.b.b 1
228.3.b.c 1
228.3.b.d 1
228.3.b.e 72
228.3.e $$\chi_{228}(77, \cdot)$$ 228.3.e.a 12 1
228.3.g $$\chi_{228}(115, \cdot)$$ 228.3.g.a 36 1
228.3.h $$\chi_{228}(37, \cdot)$$ 228.3.h.a 6 1
228.3.j $$\chi_{228}(7, \cdot)$$ 228.3.j.a 2 2
228.3.j.b 2
228.3.j.c 38
228.3.j.d 38
228.3.l $$\chi_{228}(145, \cdot)$$ 228.3.l.a 2 2
228.3.l.b 2
228.3.l.c 2
228.3.l.d 6
228.3.n $$\chi_{228}(107, \cdot)$$ 228.3.n.a 152 2
228.3.o $$\chi_{228}(125, \cdot)$$ 228.3.o.a 2 2
228.3.o.b 2
228.3.o.c 24
228.3.r $$\chi_{228}(13, \cdot)$$ 228.3.r.a 18 6
228.3.r.b 24
228.3.s $$\chi_{228}(5, \cdot)$$ 228.3.s.a 6 6
228.3.s.b 72
228.3.u $$\chi_{228}(59, \cdot)$$ 228.3.u.a 456 6
228.3.x $$\chi_{228}(43, \cdot)$$ 228.3.x.a 120 6
228.3.x.b 120

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(228))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(228)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 2}$$