## Defining parameters

 Level: $$N$$ = $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$8$$ Newform subspaces: $$19$$ Sturm bound: $$3456$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(144))$$.

Total New Old
Modular forms 1264 533 731
Cusp forms 1040 493 547
Eisenstein series 224 40 184

## Trace form

 $$493q - 6q^{2} - 6q^{3} - 12q^{4} - 15q^{5} - 8q^{6} - 23q^{7} - 10q^{9} + O(q^{10})$$ $$493q - 6q^{2} - 6q^{3} - 12q^{4} - 15q^{5} - 8q^{6} - 23q^{7} - 10q^{9} + 20q^{10} - 19q^{11} - 8q^{12} + 19q^{13} + 40q^{14} + 27q^{15} + 68q^{16} + 102q^{17} + 92q^{18} + 82q^{19} + 80q^{20} + 31q^{21} - 8q^{22} + 67q^{23} - 40q^{24} - 79q^{25} - 100q^{26} + 66q^{27} - 200q^{28} - 127q^{29} - 220q^{30} - 107q^{31} - 356q^{32} - 75q^{33} - 256q^{34} + 96q^{35} - 204q^{36} + 52q^{37} - 468q^{38} + 129q^{39} - 412q^{40} + 15q^{41} - 208q^{42} + 283q^{43} - 248q^{44} - 171q^{45} - 20q^{46} - 225q^{47} + 44q^{48} - 117q^{49} + 322q^{50} - 320q^{51} + 416q^{52} - 124q^{53} + 300q^{54} - 446q^{55} + 352q^{56} - 316q^{57} + 732q^{58} - 587q^{59} - 524q^{60} + 83q^{61} - 216q^{62} - 339q^{63} + 552q^{64} - 59q^{65} - 608q^{66} - 69q^{67} + 80q^{68} - 103q^{69} + 28q^{70} - 268q^{71} + 104q^{72} - 146q^{73} + 72q^{74} - 62q^{75} - 432q^{76} + 173q^{77} + 532q^{78} - 563q^{79} - 192q^{80} + 646q^{81} - 1544q^{82} - 283q^{83} + 520q^{84} + 308q^{85} - 72q^{86} - 69q^{87} - 844q^{88} + 426q^{89} + 280q^{90} + 142q^{91} - 500q^{92} + 567q^{93} - 84q^{94} + 714q^{95} + 60q^{96} + 429q^{97} + 838q^{98} + 747q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(144))$$

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
144.3.b $$\chi_{144}(55, \cdot)$$ None 0 1
144.3.e $$\chi_{144}(17, \cdot)$$ 144.3.e.a 2 1
144.3.e.b 2
144.3.g $$\chi_{144}(127, \cdot)$$ 144.3.g.a 1 1
144.3.g.b 2
144.3.g.c 2
144.3.h $$\chi_{144}(89, \cdot)$$ None 0 1
144.3.j $$\chi_{144}(53, \cdot)$$ 144.3.j.a 32 2
144.3.m $$\chi_{144}(19, \cdot)$$ 144.3.m.a 6 2
144.3.m.b 16
144.3.m.c 16
144.3.n $$\chi_{144}(41, \cdot)$$ None 0 2
144.3.o $$\chi_{144}(31, \cdot)$$ 144.3.o.a 8 2
144.3.o.b 8
144.3.o.c 8
144.3.q $$\chi_{144}(65, \cdot)$$ 144.3.q.a 2 2
144.3.q.b 4
144.3.q.c 4
144.3.q.d 4
144.3.q.e 8
144.3.t $$\chi_{144}(7, \cdot)$$ None 0 2
144.3.v $$\chi_{144}(43, \cdot)$$ 144.3.v.a 184 4
144.3.w $$\chi_{144}(5, \cdot)$$ 144.3.w.a 184 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(144))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(144)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 2}$$