# Properties

 Label 182.2 Level 182 Weight 2 Dimension 321 Nonzero newspaces 15 Newform subspaces 34 Sturm bound 4032 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$182 = 2 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$15$$ Newform subspaces: $$34$$ Sturm bound: $$4032$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(182))$$.

Total New Old
Modular forms 1152 321 831
Cusp forms 865 321 544
Eisenstein series 287 0 287

## Trace form

 $$321q + 3q^{2} + 8q^{3} - q^{4} + 6q^{5} - 5q^{7} - 3q^{8} - 21q^{9} + O(q^{10})$$ $$321q + 3q^{2} + 8q^{3} - q^{4} + 6q^{5} - 5q^{7} - 3q^{8} - 21q^{9} - 24q^{10} - 12q^{11} - 31q^{13} - 9q^{14} - 24q^{15} - 9q^{16} - 24q^{17} - 15q^{18} - 40q^{19} - 20q^{21} + 12q^{22} + 11q^{25} + 9q^{26} - 40q^{27} - 5q^{28} - 36q^{29} - 24q^{30} - 40q^{31} + 3q^{32} - 72q^{33} - 18q^{34} - 66q^{35} - 37q^{36} - 28q^{37} - 48q^{38} - 60q^{39} + 6q^{40} - 72q^{41} - 36q^{42} - 60q^{43} - 36q^{44} - 72q^{45} - 24q^{46} - 24q^{47} + 8q^{48} - 33q^{49} - 33q^{50} - 48q^{51} + 3q^{52} - 30q^{53} - 24q^{54} - 48q^{55} - 9q^{56} - 40q^{57} - 36q^{58} - 24q^{59} - 24q^{60} - 32q^{61} - 48q^{62} - 113q^{63} - 7q^{64} - 96q^{65} - 48q^{66} - 76q^{67} - 144q^{69} - 30q^{70} - 72q^{71} - 33q^{72} - 82q^{73} + 36q^{74} - 24q^{75} + 56q^{76} + 108q^{77} + 84q^{78} + 160q^{79} + 207q^{81} + 240q^{82} + 120q^{83} + 148q^{84} + 294q^{85} + 156q^{86} + 288q^{87} + 12q^{88} + 198q^{89} + 318q^{90} + 253q^{91} + 120q^{92} + 200q^{93} + 264q^{94} + 264q^{95} + 350q^{97} + 99q^{98} + 372q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$

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
182.2.a $$\chi_{182}(1, \cdot)$$ 182.2.a.a 1 1
182.2.a.b 1
182.2.a.c 1
182.2.a.d 1
182.2.a.e 1
182.2.d $$\chi_{182}(155, \cdot)$$ 182.2.d.a 2 1
182.2.d.b 6
182.2.e $$\chi_{182}(107, \cdot)$$ 182.2.e.a 2 2
182.2.e.b 2
182.2.e.c 6
182.2.e.d 10
182.2.f $$\chi_{182}(53, \cdot)$$ 182.2.f.a 2 2
182.2.f.b 6
182.2.f.c 8
182.2.g $$\chi_{182}(29, \cdot)$$ 182.2.g.a 2 2
182.2.g.b 2
182.2.g.c 2
182.2.g.d 2
182.2.g.e 4
182.2.h $$\chi_{182}(9, \cdot)$$ 182.2.h.a 2 2
182.2.h.b 2
182.2.h.c 6
182.2.h.d 10
182.2.i $$\chi_{182}(83, \cdot)$$ 182.2.i.a 24 2
182.2.m $$\chi_{182}(43, \cdot)$$ 182.2.m.a 4 2
182.2.m.b 12
182.2.n $$\chi_{182}(25, \cdot)$$ 182.2.n.a 4 2
182.2.n.b 12
182.2.o $$\chi_{182}(23, \cdot)$$ 182.2.o.a 20 2
182.2.v $$\chi_{182}(121, \cdot)$$ 182.2.v.a 20 2
182.2.w $$\chi_{182}(19, \cdot)$$ 182.2.w.a 40 4
182.2.ba $$\chi_{182}(41, \cdot)$$ 182.2.ba.a 32 4
182.2.bb $$\chi_{182}(5, \cdot)$$ 182.2.bb.a 32 4
182.2.bc $$\chi_{182}(45, \cdot)$$ 182.2.bc.a 40 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(182))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(182)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 2}$$