# Properties

 Label 144.4 Level 144 Weight 4 Dimension 749 Nonzero newspaces 8 Newform subspaces 26 Sturm bound 4608 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$8$$ Newform subspaces: $$26$$ Sturm bound: $$4608$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(144))$$.

Total New Old
Modular forms 1840 790 1050
Cusp forms 1616 749 867
Eisenstein series 224 41 183

## Trace form

 $$749 q - 6 q^{2} - 6 q^{3} + 4 q^{4} - 7 q^{5} - 8 q^{6} + 9 q^{7} - 48 q^{8} - 22 q^{9} + O(q^{10})$$ $$749 q - 6 q^{2} - 6 q^{3} + 4 q^{4} - 7 q^{5} - 8 q^{6} + 9 q^{7} - 48 q^{8} - 22 q^{9} - 84 q^{10} - 75 q^{11} - 8 q^{12} - 57 q^{13} + 120 q^{14} - 27 q^{15} - 252 q^{16} - 116 q^{17} - 148 q^{18} + 122 q^{19} + 416 q^{20} + 289 q^{21} + 416 q^{22} + 319 q^{23} + 728 q^{24} + 675 q^{25} + 820 q^{26} - 384 q^{27} + 408 q^{28} - 287 q^{29} - 508 q^{30} + 111 q^{31} - 996 q^{32} - 63 q^{33} - 960 q^{34} - 558 q^{35} + 756 q^{36} - 960 q^{37} + 1172 q^{38} - 231 q^{39} - 764 q^{40} - 117 q^{41} - 688 q^{42} + 1477 q^{43} - 2216 q^{44} - 273 q^{45} - 1828 q^{46} + 3813 q^{47} - 2452 q^{48} + 1477 q^{49} - 3606 q^{50} + 1954 q^{51} - 1968 q^{52} - 626 q^{53} - 228 q^{54} - 2006 q^{55} + 2880 q^{56} + 1148 q^{57} + 2260 q^{58} - 4345 q^{59} + 7924 q^{60} - 1161 q^{61} + 4728 q^{62} - 2547 q^{63} + 1576 q^{64} - 1899 q^{65} - 4928 q^{66} + 2843 q^{67} - 3440 q^{68} - 2863 q^{69} + 3468 q^{70} + 1784 q^{71} - 7960 q^{72} + 5862 q^{73} - 4096 q^{74} - 530 q^{75} + 1216 q^{76} - 5323 q^{77} - 524 q^{78} - 1159 q^{79} + 6688 q^{80} - 494 q^{81} + 3432 q^{82} - 1521 q^{83} + 9544 q^{84} - 5330 q^{85} + 8800 q^{86} - 249 q^{87} - 4812 q^{88} + 804 q^{89} + 1144 q^{90} - 5370 q^{91} - 12500 q^{92} + 861 q^{93} - 12116 q^{94} - 1372 q^{95} - 6468 q^{96} + 2545 q^{97} - 14474 q^{98} - 1575 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(144))$$

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
144.4.a $$\chi_{144}(1, \cdot)$$ 144.4.a.a 1 1
144.4.a.b 1
144.4.a.c 1
144.4.a.d 1
144.4.a.e 1
144.4.a.f 1
144.4.a.g 1
144.4.c $$\chi_{144}(143, \cdot)$$ 144.4.c.a 2 1
144.4.c.b 4
144.4.d $$\chi_{144}(73, \cdot)$$ None 0 1
144.4.f $$\chi_{144}(71, \cdot)$$ None 0 1
144.4.i $$\chi_{144}(49, \cdot)$$ 144.4.i.a 2 2
144.4.i.b 4
144.4.i.c 4
144.4.i.d 6
144.4.i.e 8
144.4.i.f 10
144.4.k $$\chi_{144}(37, \cdot)$$ 144.4.k.a 10 2
144.4.k.b 24
144.4.k.c 24
144.4.l $$\chi_{144}(35, \cdot)$$ 144.4.l.a 48 2
144.4.p $$\chi_{144}(23, \cdot)$$ None 0 2
144.4.r $$\chi_{144}(25, \cdot)$$ None 0 2
144.4.s $$\chi_{144}(47, \cdot)$$ 144.4.s.a 2 2
144.4.s.b 2
144.4.s.c 10
144.4.s.d 10
144.4.s.e 12
144.4.u $$\chi_{144}(11, \cdot)$$ 144.4.u.a 280 4
144.4.x $$\chi_{144}(13, \cdot)$$ 144.4.x.a 280 4

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(144))$$ into lower level spaces

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