## Defining parameters

 Level: $$N$$ = $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$22$$ Sturm bound: $$2304$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(144))$$.

Total New Old
Modular forms 688 277 411
Cusp forms 465 236 229
Eisenstein series 223 41 182

## Trace form

 $$236q - 6q^{2} - 6q^{3} - 4q^{4} - 5q^{5} - 8q^{6} + q^{7} + 2q^{9} + O(q^{10})$$ $$236q - 6q^{2} - 6q^{3} - 4q^{4} - 5q^{5} - 8q^{6} + q^{7} + 2q^{9} - 16q^{10} + 9q^{11} - 8q^{12} + q^{13} - 24q^{14} - 3q^{15} - 28q^{16} - 22q^{17} - 28q^{18} - 10q^{19} - 56q^{20} - 23q^{21} - 52q^{22} - 25q^{23} - 40q^{24} - 28q^{25} - 64q^{26} - 24q^{27} - 56q^{28} - 37q^{29} - 28q^{30} - 17q^{31} - 36q^{32} - 39q^{33} - 16q^{34} - 78q^{35} - 12q^{36} - 14q^{37} + 40q^{38} - 63q^{39} + 52q^{40} - 15q^{41} + 32q^{42} - 63q^{43} + 80q^{44} - 33q^{45} + 44q^{46} - 75q^{47} + 44q^{48} + 20q^{49} + 78q^{50} - 38q^{51} + 56q^{52} - 16q^{53} + 36q^{54} - 78q^{55} + 96q^{56} + 20q^{57} + 32q^{58} - 29q^{59} + 100q^{60} - 31q^{61} + 96q^{62} - 3q^{63} - 88q^{64} + 81q^{65} + 112q^{66} + 7q^{67} + 80q^{68} + 65q^{69} - 44q^{70} + 64q^{71} + 104q^{72} - 20q^{73} + 52q^{74} + 46q^{75} - 40q^{76} + 37q^{77} + 100q^{78} + 41q^{79} + 128q^{80} + 58q^{81} - 8q^{82} + 99q^{83} + 136q^{84} - 38q^{85} + 140q^{86} + 63q^{87} + 68q^{88} + 18q^{89} + 136q^{90} + 70q^{91} + 92q^{92} - 51q^{93} + 92q^{94} + 100q^{95} + 60q^{96} - 25q^{97} + 86q^{98} + 9q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
144.2.a $$\chi_{144}(1, \cdot)$$ 144.2.a.a 1 1
144.2.a.b 1
144.2.c $$\chi_{144}(143, \cdot)$$ 144.2.c.a 2 1
144.2.d $$\chi_{144}(73, \cdot)$$ None 0 1
144.2.f $$\chi_{144}(71, \cdot)$$ None 0 1
144.2.i $$\chi_{144}(49, \cdot)$$ 144.2.i.a 2 2
144.2.i.b 2
144.2.i.c 2
144.2.i.d 4
144.2.k $$\chi_{144}(37, \cdot)$$ 144.2.k.a 2 2
144.2.k.b 8
144.2.k.c 8
144.2.l $$\chi_{144}(35, \cdot)$$ 144.2.l.a 16 2
144.2.p $$\chi_{144}(23, \cdot)$$ None 0 2
144.2.r $$\chi_{144}(25, \cdot)$$ None 0 2
144.2.s $$\chi_{144}(47, \cdot)$$ 144.2.s.a 2 2
144.2.s.b 2
144.2.s.c 2
144.2.s.d 2
144.2.s.e 4
144.2.u $$\chi_{144}(11, \cdot)$$ 144.2.u.a 88 4
144.2.x $$\chi_{144}(13, \cdot)$$ 144.2.x.a 4 4
144.2.x.b 4
144.2.x.c 4
144.2.x.d 4
144.2.x.e 72

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(144))$$ into lower level spaces

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