# Properties

 Label 72.3 Level 72 Weight 3 Dimension 119 Nonzero newspaces 6 Newform subspaces 10 Sturm bound 864 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$10$$ Sturm bound: $$864$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(72))$$.

Total New Old
Modular forms 336 137 199
Cusp forms 240 119 121
Eisenstein series 96 18 78

## Trace form

 $$119 q - 4 q^{2} - 6 q^{3} + 2 q^{4} + 4 q^{6} + 22 q^{7} + 26 q^{8} + 6 q^{9} + O(q^{10})$$ $$119 q - 4 q^{2} - 6 q^{3} + 2 q^{4} + 4 q^{6} + 22 q^{7} + 26 q^{8} + 6 q^{9} + 8 q^{10} + 34 q^{11} - 14 q^{12} - 16 q^{13} - 78 q^{14} + 6 q^{15} - 122 q^{16} - 2 q^{17} - 96 q^{18} + 2 q^{19} - 150 q^{20} - 36 q^{21} - 38 q^{22} - 78 q^{23} - 24 q^{24} + q^{25} + 24 q^{26} - 180 q^{27} + 168 q^{28} - 108 q^{29} - 74 q^{30} - 114 q^{31} + 86 q^{32} - 22 q^{33} + 102 q^{34} - 204 q^{35} + 2 q^{36} + 60 q^{37} - 110 q^{38} + 6 q^{39} - 326 q^{40} + 172 q^{41} + 194 q^{42} - 150 q^{43} + 130 q^{44} + 260 q^{45} - 40 q^{46} + 318 q^{47} + 332 q^{48} + 153 q^{49} + 530 q^{50} + 210 q^{51} + 374 q^{52} + 288 q^{54} + 404 q^{55} + 624 q^{56} - 290 q^{57} + 294 q^{58} - 62 q^{59} + 606 q^{60} - 76 q^{61} + 180 q^{62} - 490 q^{63} - 436 q^{64} - 636 q^{65} + 172 q^{66} - 94 q^{67} - 20 q^{68} - 104 q^{69} - 58 q^{70} - 78 q^{72} - 354 q^{73} + 6 q^{74} + 454 q^{75} + 182 q^{76} + 504 q^{77} - 446 q^{78} - 246 q^{79} - 624 q^{80} + 398 q^{81} + 8 q^{82} + 100 q^{83} - 952 q^{84} - 188 q^{85} - 998 q^{86} + 138 q^{87} - 626 q^{88} - 50 q^{89} - 1250 q^{90} - 780 q^{91} - 1098 q^{92} - 352 q^{93} - 828 q^{94} - 684 q^{95} - 888 q^{96} - 252 q^{97} - 1078 q^{98} - 510 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(72))$$

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
72.3.b $$\chi_{72}(19, \cdot)$$ 72.3.b.a 1 1
72.3.b.b 4
72.3.b.c 4
72.3.e $$\chi_{72}(17, \cdot)$$ 72.3.e.a 2 1
72.3.g $$\chi_{72}(55, \cdot)$$ None 0 1
72.3.h $$\chi_{72}(53, \cdot)$$ 72.3.h.a 8 1
72.3.j $$\chi_{72}(5, \cdot)$$ 72.3.j.a 44 2
72.3.k $$\chi_{72}(7, \cdot)$$ None 0 2
72.3.m $$\chi_{72}(41, \cdot)$$ 72.3.m.a 4 2
72.3.m.b 8
72.3.p $$\chi_{72}(43, \cdot)$$ 72.3.p.a 4 2
72.3.p.b 40

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(72))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(72)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 2}$$