# Properties

 Label 729.2 Level 729 Weight 2 Dimension 15228 Nonzero newspaces 6 Newform subspaces 37 Sturm bound 78732 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$729 = 3^{6}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$37$$ Sturm bound: $$78732$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(729))$$.

Total New Old
Modular forms 20331 15876 4455
Cusp forms 19036 15228 3808
Eisenstein series 1295 648 647

## Trace form

 $$15228 q - 108 q^{2} - 162 q^{3} - 180 q^{4} - 108 q^{5} - 162 q^{6} - 180 q^{7} - 108 q^{8} - 162 q^{9} + O(q^{10})$$ $$15228 q - 108 q^{2} - 162 q^{3} - 180 q^{4} - 108 q^{5} - 162 q^{6} - 180 q^{7} - 108 q^{8} - 162 q^{9} - 252 q^{10} - 108 q^{11} - 162 q^{12} - 180 q^{13} - 108 q^{14} - 162 q^{15} - 180 q^{16} - 108 q^{17} - 162 q^{18} - 252 q^{19} - 108 q^{20} - 162 q^{21} - 180 q^{22} - 108 q^{23} - 162 q^{24} - 180 q^{25} - 108 q^{26} - 162 q^{27} - 324 q^{28} - 108 q^{29} - 162 q^{30} - 180 q^{31} - 108 q^{32} - 162 q^{33} - 180 q^{34} - 108 q^{35} - 162 q^{36} - 252 q^{37} - 108 q^{38} - 162 q^{39} - 180 q^{40} - 108 q^{41} - 162 q^{42} - 180 q^{43} - 108 q^{44} - 162 q^{45} - 252 q^{46} - 108 q^{47} - 162 q^{48} - 180 q^{49} - 108 q^{50} - 162 q^{51} - 216 q^{52} - 108 q^{53} - 162 q^{54} - 324 q^{55} - 108 q^{56} - 162 q^{57} - 180 q^{58} - 108 q^{59} - 162 q^{60} - 180 q^{61} - 108 q^{62} - 162 q^{63} - 324 q^{64} - 162 q^{65} - 162 q^{66} - 234 q^{67} - 297 q^{68} - 162 q^{69} - 288 q^{70} - 216 q^{71} - 162 q^{72} - 333 q^{73} - 324 q^{74} - 162 q^{75} - 342 q^{76} - 324 q^{77} - 162 q^{78} - 288 q^{79} - 513 q^{80} - 162 q^{81} - 567 q^{82} - 216 q^{83} - 162 q^{84} - 288 q^{85} - 324 q^{86} - 162 q^{87} - 342 q^{88} - 243 q^{89} - 162 q^{90} - 333 q^{91} - 432 q^{92} - 162 q^{93} - 288 q^{94} - 216 q^{95} - 162 q^{96} - 234 q^{97} - 216 q^{98} - 162 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(729))$$

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
729.2.a $$\chi_{729}(1, \cdot)$$ 729.2.a.a 6 1
729.2.a.b 6
729.2.a.c 6
729.2.a.d 6
729.2.a.e 6
729.2.c $$\chi_{729}(244, \cdot)$$ 729.2.c.a 12 2
729.2.c.b 12
729.2.c.c 12
729.2.c.d 12
729.2.c.e 12
729.2.e $$\chi_{729}(82, \cdot)$$ 729.2.e.a 6 6
729.2.e.b 6
729.2.e.c 6
729.2.e.d 6
729.2.e.e 6
729.2.e.f 6
729.2.e.g 6
729.2.e.h 6
729.2.e.i 6
729.2.e.j 12
729.2.e.k 12
729.2.e.l 12
729.2.e.m 12
729.2.e.n 12
729.2.e.o 12
729.2.e.p 12
729.2.e.q 12
729.2.e.r 12
729.2.e.s 12
729.2.e.t 12
729.2.e.u 12
729.2.g $$\chi_{729}(28, \cdot)$$ 729.2.g.a 144 18
729.2.g.b 144
729.2.g.c 144
729.2.g.d 144
729.2.i $$\chi_{729}(10, \cdot)$$ 729.2.i.a 1404 54
729.2.k $$\chi_{729}(4, \cdot)$$ 729.2.k.a 12960 162

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(729))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(729)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(243))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(729))$$$$^{\oplus 1}$$