# Properties

 Label 150.3 Level 150 Weight 3 Dimension 276 Nonzero newspaces 6 Newform subspaces 13 Sturm bound 3600 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$13$$ Sturm bound: $$3600$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(150))$$.

Total New Old
Modular forms 1312 276 1036
Cusp forms 1088 276 812
Eisenstein series 224 0 224

## Trace form

 $$276 q - 8 q^{2} - 8 q^{3} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 80 q^{9} + O(q^{10})$$ $$276 q - 8 q^{2} - 8 q^{3} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 80 q^{9} + 12 q^{10} + 32 q^{11} + 16 q^{12} + 56 q^{13} - 4 q^{15} - 32 q^{16} + 192 q^{17} - 28 q^{18} + 240 q^{19} + 32 q^{20} - 8 q^{21} + 96 q^{22} + 112 q^{23} - 156 q^{25} - 128 q^{26} - 56 q^{27} - 192 q^{28} - 400 q^{29} - 240 q^{30} - 208 q^{31} - 48 q^{32} - 312 q^{33} - 180 q^{34} - 328 q^{35} + 48 q^{36} + 512 q^{37} + 128 q^{38} + 480 q^{39} + 24 q^{40} + 256 q^{41} + 160 q^{42} + 272 q^{43} + 380 q^{45} - 160 q^{46} - 32 q^{47} - 32 q^{48} - 480 q^{49} - 92 q^{50} - 424 q^{51} - 208 q^{52} - 560 q^{53} - 480 q^{54} - 944 q^{55} - 128 q^{56} - 1040 q^{57} - 128 q^{58} - 800 q^{59} - 208 q^{60} - 32 q^{61} + 160 q^{62} - 1052 q^{63} + 44 q^{65} + 160 q^{66} + 688 q^{67} + 176 q^{68} - 300 q^{69} + 48 q^{70} - 128 q^{71} + 80 q^{72} - 24 q^{73} + 404 q^{75} + 192 q^{76} + 256 q^{77} + 128 q^{78} + 800 q^{79} + 200 q^{81} - 448 q^{82} + 256 q^{83} + 120 q^{84} + 744 q^{85} - 192 q^{86} + 1396 q^{87} + 128 q^{88} + 100 q^{89} + 924 q^{90} + 224 q^{91} + 64 q^{92} + 748 q^{93} + 640 q^{94} + 256 q^{95} + 64 q^{96} - 776 q^{97} + 248 q^{98} - 160 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(150))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
150.3.b $$\chi_{150}(149, \cdot)$$ 150.3.b.a 4 1
150.3.b.b 8
150.3.d $$\chi_{150}(101, \cdot)$$ 150.3.d.a 2 1
150.3.d.b 2
150.3.d.c 4
150.3.d.d 4
150.3.f $$\chi_{150}(7, \cdot)$$ 150.3.f.a 4 2
150.3.f.b 4
150.3.f.c 4
150.3.i $$\chi_{150}(29, \cdot)$$ 150.3.i.a 80 4
150.3.j $$\chi_{150}(11, \cdot)$$ 150.3.j.a 80 4
150.3.k $$\chi_{150}(13, \cdot)$$ 150.3.k.a 32 8
150.3.k.b 48

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(150))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(150)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 1}$$