# Properties

 Label 153.2 Level 153 Weight 2 Dimension 612 Nonzero newspaces 10 Newform subspaces 25 Sturm bound 3456 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$153 = 3^{2} \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Newform subspaces: $$25$$ Sturm bound: $$3456$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(153))$$.

Total New Old
Modular forms 992 746 246
Cusp forms 737 612 125
Eisenstein series 255 134 121

## Trace form

 $$612 q - 24 q^{2} - 32 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 24 q^{7} - 24 q^{8} - 32 q^{9} + O(q^{10})$$ $$612 q - 24 q^{2} - 32 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 24 q^{7} - 24 q^{8} - 32 q^{9} - 76 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 40 q^{14} - 32 q^{15} - 60 q^{16} - 32 q^{17} - 64 q^{18} - 80 q^{19} - 52 q^{20} - 32 q^{21} - 40 q^{22} - 32 q^{23} - 32 q^{24} - 52 q^{25} - 60 q^{26} - 32 q^{27} - 120 q^{28} - 44 q^{29} - 32 q^{30} - 56 q^{31} - 16 q^{32} - 32 q^{33} - 88 q^{34} - 80 q^{35} - 32 q^{36} - 104 q^{37} - 40 q^{38} + 8 q^{40} + 28 q^{41} + 64 q^{42} + 136 q^{44} + 32 q^{45} + 8 q^{46} + 96 q^{47} + 128 q^{48} + 72 q^{49} + 168 q^{50} + 32 q^{51} + 144 q^{52} + 60 q^{53} + 80 q^{54} - 8 q^{55} + 176 q^{56} + 48 q^{57} + 16 q^{58} + 40 q^{59} + 96 q^{60} - 24 q^{61} + 64 q^{62} + 16 q^{63} - 56 q^{64} - 36 q^{65} + 16 q^{66} - 64 q^{67} - 124 q^{68} - 64 q^{69} - 160 q^{70} - 72 q^{71} + 32 q^{72} - 172 q^{73} - 108 q^{74} - 32 q^{75} - 144 q^{76} - 104 q^{77} - 32 q^{78} - 88 q^{79} - 40 q^{80} - 32 q^{81} - 180 q^{82} - 56 q^{83} + 48 q^{84} + 12 q^{85} + 160 q^{86} + 64 q^{87} + 72 q^{88} + 96 q^{89} + 208 q^{90} + 72 q^{91} + 232 q^{92} + 96 q^{93} + 200 q^{94} + 184 q^{95} + 272 q^{96} + 40 q^{97} + 348 q^{98} + 112 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(153))$$

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
153.2.a $$\chi_{153}(1, \cdot)$$ 153.2.a.a 1 1
153.2.a.b 1
153.2.a.c 1
153.2.a.d 1
153.2.a.e 2
153.2.d $$\chi_{153}(118, \cdot)$$ 153.2.d.a 2 1
153.2.d.b 2
153.2.d.c 2
153.2.e $$\chi_{153}(52, \cdot)$$ 153.2.e.a 4 2
153.2.e.b 8
153.2.e.c 20
153.2.f $$\chi_{153}(55, \cdot)$$ 153.2.f.a 4 2
153.2.f.b 8
153.2.h $$\chi_{153}(16, \cdot)$$ 153.2.h.a 8 2
153.2.h.b 24
153.2.l $$\chi_{153}(19, \cdot)$$ 153.2.l.a 4 4
153.2.l.b 4
153.2.l.c 4
153.2.l.d 8
153.2.l.e 8
153.2.n $$\chi_{153}(4, \cdot)$$ 153.2.n.a 64 4
153.2.o $$\chi_{153}(44, \cdot)$$ 153.2.o.a 24 8
153.2.o.b 24
153.2.r $$\chi_{153}(25, \cdot)$$ 153.2.r.a 128 8
153.2.s $$\chi_{153}(5, \cdot)$$ 153.2.s.a 256 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(153))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(153)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 2}$$