# Properties

 Label 126.2 Level 126 Weight 2 Dimension 110 Nonzero newspaces 9 Newforms 22 Sturm bound 1728 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$9$$ Newforms: $$22$$ Sturm bound: $$1728$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(126))$$.

Total New Old
Modular forms 528 110 418
Cusp forms 337 110 227
Eisenstein series 191 0 191

## Trace form

 $$110q$$ $$\mathstrut +\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 6q^{3}$$ $$\mathstrut +\mathstrut 4q^{4}$$ $$\mathstrut +\mathstrut 6q^{5}$$ $$\mathstrut -\mathstrut 6q^{6}$$ $$\mathstrut +\mathstrut 10q^{7}$$ $$\mathstrut -\mathstrut 4q^{8}$$ $$\mathstrut -\mathstrut 6q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$110q$$ $$\mathstrut +\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 6q^{3}$$ $$\mathstrut +\mathstrut 4q^{4}$$ $$\mathstrut +\mathstrut 6q^{5}$$ $$\mathstrut -\mathstrut 6q^{6}$$ $$\mathstrut +\mathstrut 10q^{7}$$ $$\mathstrut -\mathstrut 4q^{8}$$ $$\mathstrut -\mathstrut 6q^{9}$$ $$\mathstrut +\mathstrut 6q^{10}$$ $$\mathstrut +\mathstrut 6q^{11}$$ $$\mathstrut +\mathstrut 6q^{13}$$ $$\mathstrut -\mathstrut 16q^{14}$$ $$\mathstrut -\mathstrut 24q^{15}$$ $$\mathstrut -\mathstrut 4q^{16}$$ $$\mathstrut -\mathstrut 36q^{17}$$ $$\mathstrut -\mathstrut 12q^{18}$$ $$\mathstrut -\mathstrut 30q^{19}$$ $$\mathstrut -\mathstrut 18q^{20}$$ $$\mathstrut -\mathstrut 42q^{21}$$ $$\mathstrut -\mathstrut 42q^{22}$$ $$\mathstrut -\mathstrut 60q^{23}$$ $$\mathstrut -\mathstrut 6q^{24}$$ $$\mathstrut -\mathstrut 40q^{25}$$ $$\mathstrut -\mathstrut 38q^{26}$$ $$\mathstrut -\mathstrut 36q^{27}$$ $$\mathstrut -\mathstrut 4q^{28}$$ $$\mathstrut -\mathstrut 12q^{29}$$ $$\mathstrut -\mathstrut 12q^{30}$$ $$\mathstrut -\mathstrut 12q^{31}$$ $$\mathstrut +\mathstrut 2q^{32}$$ $$\mathstrut -\mathstrut 6q^{33}$$ $$\mathstrut +\mathstrut 6q^{34}$$ $$\mathstrut -\mathstrut 30q^{35}$$ $$\mathstrut -\mathstrut 6q^{36}$$ $$\mathstrut +\mathstrut 8q^{37}$$ $$\mathstrut +\mathstrut 16q^{38}$$ $$\mathstrut -\mathstrut 36q^{39}$$ $$\mathstrut +\mathstrut 6q^{40}$$ $$\mathstrut -\mathstrut 30q^{41}$$ $$\mathstrut +\mathstrut 2q^{43}$$ $$\mathstrut +\mathstrut 24q^{44}$$ $$\mathstrut -\mathstrut 48q^{45}$$ $$\mathstrut +\mathstrut 48q^{46}$$ $$\mathstrut -\mathstrut 48q^{47}$$ $$\mathstrut -\mathstrut 6q^{48}$$ $$\mathstrut -\mathstrut 28q^{49}$$ $$\mathstrut +\mathstrut 50q^{50}$$ $$\mathstrut +\mathstrut 18q^{51}$$ $$\mathstrut -\mathstrut 6q^{52}$$ $$\mathstrut +\mathstrut 24q^{53}$$ $$\mathstrut +\mathstrut 54q^{54}$$ $$\mathstrut +\mathstrut 8q^{56}$$ $$\mathstrut +\mathstrut 90q^{57}$$ $$\mathstrut -\mathstrut 12q^{58}$$ $$\mathstrut +\mathstrut 120q^{59}$$ $$\mathstrut +\mathstrut 72q^{60}$$ $$\mathstrut -\mathstrut 6q^{61}$$ $$\mathstrut +\mathstrut 100q^{62}$$ $$\mathstrut +\mathstrut 180q^{63}$$ $$\mathstrut -\mathstrut 2q^{64}$$ $$\mathstrut +\mathstrut 168q^{65}$$ $$\mathstrut +\mathstrut 96q^{66}$$ $$\mathstrut -\mathstrut 26q^{67}$$ $$\mathstrut +\mathstrut 54q^{68}$$ $$\mathstrut +\mathstrut 108q^{69}$$ $$\mathstrut -\mathstrut 18q^{70}$$ $$\mathstrut +\mathstrut 120q^{71}$$ $$\mathstrut -\mathstrut 6q^{72}$$ $$\mathstrut -\mathstrut 24q^{73}$$ $$\mathstrut +\mathstrut 64q^{74}$$ $$\mathstrut +\mathstrut 114q^{75}$$ $$\mathstrut +\mathstrut 66q^{77}$$ $$\mathstrut +\mathstrut 60q^{78}$$ $$\mathstrut +\mathstrut 4q^{79}$$ $$\mathstrut +\mathstrut 6q^{80}$$ $$\mathstrut +\mathstrut 6q^{81}$$ $$\mathstrut +\mathstrut 30q^{83}$$ $$\mathstrut +\mathstrut 6q^{84}$$ $$\mathstrut +\mathstrut 60q^{85}$$ $$\mathstrut +\mathstrut 10q^{86}$$ $$\mathstrut -\mathstrut 108q^{87}$$ $$\mathstrut -\mathstrut 18q^{88}$$ $$\mathstrut -\mathstrut 84q^{89}$$ $$\mathstrut -\mathstrut 48q^{90}$$ $$\mathstrut -\mathstrut 66q^{91}$$ $$\mathstrut -\mathstrut 36q^{92}$$ $$\mathstrut -\mathstrut 108q^{93}$$ $$\mathstrut -\mathstrut 48q^{94}$$ $$\mathstrut -\mathstrut 144q^{95}$$ $$\mathstrut -\mathstrut 12q^{96}$$ $$\mathstrut -\mathstrut 54q^{97}$$ $$\mathstrut -\mathstrut 76q^{98}$$ $$\mathstrut -\mathstrut 156q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$

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
126.2.a $$\chi_{126}(1, \cdot)$$ 126.2.a.a 1 1
126.2.a.b 1
126.2.d $$\chi_{126}(125, \cdot)$$ None 0 1
126.2.e $$\chi_{126}(25, \cdot)$$ 126.2.e.a 2 2
126.2.e.b 2
126.2.e.c 6
126.2.e.d 6
126.2.f $$\chi_{126}(43, \cdot)$$ 126.2.f.a 2 2
126.2.f.b 2
126.2.f.c 4
126.2.f.d 4
126.2.g $$\chi_{126}(37, \cdot)$$ 126.2.g.a 2 2
126.2.g.b 2
126.2.g.c 2
126.2.g.d 2
126.2.h $$\chi_{126}(67, \cdot)$$ 126.2.h.a 2 2
126.2.h.b 2
126.2.h.c 6
126.2.h.d 6
126.2.k $$\chi_{126}(17, \cdot)$$ 126.2.k.a 8 2
126.2.l $$\chi_{126}(5, \cdot)$$ 126.2.l.a 16 2
126.2.m $$\chi_{126}(41, \cdot)$$ 126.2.m.a 16 2
126.2.t $$\chi_{126}(47, \cdot)$$ 126.2.t.a 16 2

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(126))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(126)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$