# Properties

 Label 120.4 Level 120 Weight 4 Dimension 436 Nonzero newspaces 9 Newform subspaces 24 Sturm bound 3072 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$9$$ Newform subspaces: $$24$$ Sturm bound: $$3072$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(120))$$.

Total New Old
Modular forms 1248 460 788
Cusp forms 1056 436 620
Eisenstein series 192 24 168

## Trace form

 $$436 q - 4 q^{2} - 6 q^{3} - 48 q^{4} + 8 q^{5} + 20 q^{6} - 40 q^{7} + 152 q^{8} + 68 q^{9} + O(q^{10})$$ $$436 q - 4 q^{2} - 6 q^{3} - 48 q^{4} + 8 q^{5} + 20 q^{6} - 40 q^{7} + 152 q^{8} + 68 q^{9} - 44 q^{10} + 40 q^{13} - 64 q^{14} + 86 q^{15} + 400 q^{16} - 96 q^{17} + 140 q^{18} + 312 q^{19} + 704 q^{20} + 176 q^{21} - 384 q^{22} - 504 q^{23} - 1096 q^{24} + 532 q^{25} - 848 q^{26} + 42 q^{27} - 1120 q^{28} - 576 q^{29} + 564 q^{30} + 40 q^{31} + 1176 q^{32} + 456 q^{33} + 2080 q^{34} + 1248 q^{35} + 1832 q^{36} + 1144 q^{37} - 520 q^{38} + 1068 q^{39} - 2112 q^{40} + 312 q^{41} - 2760 q^{42} + 744 q^{43} - 3368 q^{44} - 536 q^{45} - 3360 q^{46} - 1168 q^{47} - 1496 q^{48} - 3364 q^{49} + 620 q^{50} - 4308 q^{51} + 248 q^{52} - 1264 q^{53} + 2716 q^{54} - 816 q^{55} + 3728 q^{56} - 1136 q^{57} + 4944 q^{58} + 120 q^{59} + 504 q^{60} + 2168 q^{61} + 4216 q^{62} + 1568 q^{63} + 6960 q^{64} - 896 q^{65} - 368 q^{66} + 5816 q^{67} - 2984 q^{68} - 1152 q^{69} - 4264 q^{70} + 176 q^{71} - 5432 q^{72} - 96 q^{73} - 7448 q^{74} - 1342 q^{75} - 9056 q^{76} + 96 q^{77} - 848 q^{78} - 6000 q^{79} - 4208 q^{80} + 3660 q^{81} - 1664 q^{82} - 4688 q^{83} + 3688 q^{84} + 1504 q^{85} - 8816 q^{86} - 1204 q^{87} + 1360 q^{88} - 80 q^{89} - 1492 q^{90} + 32 q^{91} + 5528 q^{92} + 3456 q^{93} + 2384 q^{94} + 6744 q^{95} + 976 q^{96} + 2600 q^{97} + 10468 q^{98} - 1896 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(120))$$

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
120.4.a $$\chi_{120}(1, \cdot)$$ 120.4.a.a 1 1
120.4.a.b 1
120.4.a.c 1
120.4.a.d 1
120.4.a.e 1
120.4.a.f 1
120.4.b $$\chi_{120}(11, \cdot)$$ 120.4.b.a 24 1
120.4.b.b 24
120.4.d $$\chi_{120}(109, \cdot)$$ 120.4.d.a 18 1
120.4.d.b 18
120.4.f $$\chi_{120}(49, \cdot)$$ 120.4.f.a 2 1
120.4.f.b 2
120.4.f.c 2
120.4.f.d 4
120.4.h $$\chi_{120}(71, \cdot)$$ None 0 1
120.4.k $$\chi_{120}(61, \cdot)$$ 120.4.k.a 2 1
120.4.k.b 8
120.4.k.c 14
120.4.m $$\chi_{120}(59, \cdot)$$ 120.4.m.a 4 1
120.4.m.b 64
120.4.o $$\chi_{120}(119, \cdot)$$ None 0 1
120.4.r $$\chi_{120}(17, \cdot)$$ 120.4.r.a 36 2
120.4.s $$\chi_{120}(7, \cdot)$$ None 0 2
120.4.v $$\chi_{120}(43, \cdot)$$ 120.4.v.a 72 2
120.4.w $$\chi_{120}(53, \cdot)$$ 120.4.w.a 4 2
120.4.w.b 4
120.4.w.c 128

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(120))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(120)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 1}$$