# Properties

 Label 147.4 Level 147 Weight 4 Dimension 1644 Nonzero newspaces 8 Newform subspaces 41 Sturm bound 6272 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$8$$ Newform subspaces: $$41$$ Sturm bound: $$6272$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(147))$$.

Total New Old
Modular forms 2472 1740 732
Cusp forms 2232 1644 588
Eisenstein series 240 96 144

## Trace form

 $$1644 q - 27 q^{3} - 30 q^{4} + 48 q^{5} + 51 q^{6} + 12 q^{7} - 108 q^{8} - 99 q^{9} + O(q^{10})$$ $$1644 q - 27 q^{3} - 30 q^{4} + 48 q^{5} + 51 q^{6} + 12 q^{7} - 108 q^{8} - 99 q^{9} - 138 q^{10} + 171 q^{12} + 126 q^{13} + 312 q^{14} + 357 q^{15} + 210 q^{16} + 24 q^{17} - 561 q^{18} - 1158 q^{19} - 2088 q^{20} - 606 q^{21} - 942 q^{22} + 336 q^{23} - 309 q^{24} + 810 q^{25} + 588 q^{26} + 195 q^{27} + 1068 q^{28} + 1296 q^{29} + 3039 q^{30} + 1458 q^{31} + 2436 q^{32} + 1581 q^{33} + 510 q^{34} - 84 q^{35} - 555 q^{36} + 1818 q^{37} + 1788 q^{38} - 387 q^{39} + 3174 q^{40} + 288 q^{41} - 2847 q^{42} - 3894 q^{43} - 11424 q^{44} - 5835 q^{45} - 12042 q^{46} - 5448 q^{47} - 5280 q^{48} - 5760 q^{49} - 1212 q^{50} + 2589 q^{51} - 1770 q^{52} + 1848 q^{53} + 8295 q^{54} + 738 q^{55} + 1326 q^{56} + 1269 q^{57} - 42 q^{58} + 5880 q^{59} + 4443 q^{60} + 4266 q^{61} + 7632 q^{62} - 1170 q^{63} + 582 q^{64} - 1008 q^{65} - 1785 q^{66} - 1878 q^{67} + 3072 q^{68} + 3291 q^{69} + 3462 q^{70} + 984 q^{71} + 8079 q^{72} + 8610 q^{73} + 5460 q^{74} + 4587 q^{75} + 11046 q^{76} + 180 q^{77} + 2841 q^{78} + 978 q^{79} + 20142 q^{80} + 6705 q^{81} + 15012 q^{82} + 10584 q^{83} + 11658 q^{84} + 498 q^{85} - 42 q^{86} - 1149 q^{87} + 348 q^{88} - 696 q^{89} - 14220 q^{90} - 10086 q^{91} - 10290 q^{92} - 18159 q^{93} - 33180 q^{94} - 33264 q^{95} - 28704 q^{96} - 16896 q^{97} - 51054 q^{98} - 7128 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(147))$$

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
147.4.a $$\chi_{147}(1, \cdot)$$ 147.4.a.a 1 1
147.4.a.b 1
147.4.a.c 1
147.4.a.d 1
147.4.a.e 1
147.4.a.f 1
147.4.a.g 1
147.4.a.h 1
147.4.a.i 2
147.4.a.j 2
147.4.a.k 2
147.4.a.l 3
147.4.a.m 3
147.4.c $$\chi_{147}(146, \cdot)$$ 147.4.c.a 12 1
147.4.c.b 24
147.4.e $$\chi_{147}(67, \cdot)$$ 147.4.e.a 2 2
147.4.e.b 2
147.4.e.c 2
147.4.e.d 2
147.4.e.e 2
147.4.e.f 2
147.4.e.g 2
147.4.e.h 2
147.4.e.i 2
147.4.e.j 4
147.4.e.k 4
147.4.e.l 4
147.4.e.m 4
147.4.e.n 6
147.4.g $$\chi_{147}(68, \cdot)$$ 147.4.g.a 2 2
147.4.g.b 2
147.4.g.c 8
147.4.g.d 12
147.4.g.e 48
147.4.i $$\chi_{147}(22, \cdot)$$ 147.4.i.a 84 6
147.4.i.b 84
147.4.k $$\chi_{147}(20, \cdot)$$ 147.4.k.a 12 6
147.4.k.b 312
147.4.m $$\chi_{147}(4, \cdot)$$ 147.4.m.a 156 12
147.4.m.b 180
147.4.o $$\chi_{147}(5, \cdot)$$ 147.4.o.a 648 12

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(147))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(147)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 1}$$