# Properties

 Label 243.2 Level 243 Weight 2 Dimension 1632 Nonzero newspaces 5 Newform subspaces 18 Sturm bound 8748 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$243 = 3^{5}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$5$$ Newform subspaces: $$18$$ Sturm bound: $$8748$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(243))$$.

Total New Old
Modular forms 2376 1824 552
Cusp forms 1999 1632 367
Eisenstein series 377 192 185

## Trace form

 $$1632 q - 36 q^{2} - 54 q^{3} - 60 q^{4} - 36 q^{5} - 54 q^{6} - 60 q^{7} - 36 q^{8} - 54 q^{9} + O(q^{10})$$ $$1632 q - 36 q^{2} - 54 q^{3} - 60 q^{4} - 36 q^{5} - 54 q^{6} - 60 q^{7} - 36 q^{8} - 54 q^{9} - 84 q^{10} - 36 q^{11} - 54 q^{12} - 60 q^{13} - 36 q^{14} - 54 q^{15} - 72 q^{16} - 36 q^{17} - 54 q^{18} - 93 q^{19} - 72 q^{20} - 54 q^{21} - 78 q^{22} - 63 q^{23} - 54 q^{24} - 78 q^{25} - 99 q^{26} - 54 q^{27} - 147 q^{28} - 63 q^{29} - 54 q^{30} - 78 q^{31} - 90 q^{32} - 54 q^{33} - 90 q^{34} - 63 q^{35} - 54 q^{36} - 93 q^{37} - 45 q^{38} - 54 q^{39} - 114 q^{40} - 54 q^{41} - 54 q^{42} - 78 q^{43} - 108 q^{44} - 54 q^{45} - 138 q^{46} - 90 q^{47} - 54 q^{48} - 96 q^{49} - 153 q^{50} - 54 q^{51} - 72 q^{52} - 99 q^{53} - 54 q^{54} - 165 q^{55} - 180 q^{56} - 54 q^{57} - 114 q^{58} - 99 q^{59} - 54 q^{60} - 96 q^{61} - 135 q^{62} - 54 q^{63} - 42 q^{64} + 54 q^{66} - 15 q^{67} + 234 q^{68} + 54 q^{69} + 12 q^{70} + 144 q^{71} + 270 q^{72} + 24 q^{73} + 324 q^{74} + 81 q^{75} + 105 q^{76} + 324 q^{77} + 162 q^{78} + 66 q^{79} + 639 q^{80} + 54 q^{81} + 105 q^{82} + 144 q^{83} + 324 q^{84} + 36 q^{85} + 324 q^{86} + 162 q^{87} + 69 q^{88} + 162 q^{89} + 162 q^{90} - 12 q^{91} + 414 q^{92} + 54 q^{93} + 12 q^{94} + 36 q^{95} + 135 q^{96} - 51 q^{97} - 27 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(243))$$

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
243.2.a $$\chi_{243}(1, \cdot)$$ 243.2.a.a 1 1
243.2.a.b 1
243.2.a.c 2
243.2.a.d 2
243.2.a.e 3
243.2.a.f 3
243.2.c $$\chi_{243}(82, \cdot)$$ 243.2.c.a 2 2
243.2.c.b 2
243.2.c.c 4
243.2.c.d 4
243.2.c.e 6
243.2.c.f 6
243.2.e $$\chi_{243}(28, \cdot)$$ 243.2.e.a 12 6
243.2.e.b 12
243.2.e.c 12
243.2.e.d 12
243.2.g $$\chi_{243}(10, \cdot)$$ 243.2.g.a 144 18
243.2.i $$\chi_{243}(4, \cdot)$$ 243.2.i.a 1404 54

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(243))$$ into lower level spaces

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