# Properties

 Label 63.2 Level 63 Weight 2 Dimension 87 Nonzero newspaces 10 Newforms 17 Sturm bound 576 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Newforms: $$17$$ Sturm bound: $$576$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(63))$$.

Total New Old
Modular forms 192 131 61
Cusp forms 97 87 10
Eisenstein series 95 44 51

## Trace form

 $$87q$$ $$\mathstrut -\mathstrut 9q^{2}$$ $$\mathstrut -\mathstrut 12q^{3}$$ $$\mathstrut -\mathstrut 13q^{4}$$ $$\mathstrut -\mathstrut 12q^{5}$$ $$\mathstrut -\mathstrut 12q^{6}$$ $$\mathstrut -\mathstrut 13q^{7}$$ $$\mathstrut -\mathstrut 27q^{8}$$ $$\mathstrut -\mathstrut 12q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$87q$$ $$\mathstrut -\mathstrut 9q^{2}$$ $$\mathstrut -\mathstrut 12q^{3}$$ $$\mathstrut -\mathstrut 13q^{4}$$ $$\mathstrut -\mathstrut 12q^{5}$$ $$\mathstrut -\mathstrut 12q^{6}$$ $$\mathstrut -\mathstrut 13q^{7}$$ $$\mathstrut -\mathstrut 27q^{8}$$ $$\mathstrut -\mathstrut 12q^{9}$$ $$\mathstrut -\mathstrut 42q^{10}$$ $$\mathstrut -\mathstrut 18q^{11}$$ $$\mathstrut -\mathstrut 16q^{13}$$ $$\mathstrut -\mathstrut 3q^{14}$$ $$\mathstrut -\mathstrut 12q^{15}$$ $$\mathstrut +\mathstrut 3q^{16}$$ $$\mathstrut +\mathstrut 12q^{17}$$ $$\mathstrut +\mathstrut 12q^{18}$$ $$\mathstrut -\mathstrut 16q^{19}$$ $$\mathstrut +\mathstrut 36q^{20}$$ $$\mathstrut +\mathstrut 6q^{21}$$ $$\mathstrut +\mathstrut 6q^{23}$$ $$\mathstrut +\mathstrut 24q^{24}$$ $$\mathstrut -\mathstrut 9q^{25}$$ $$\mathstrut +\mathstrut 24q^{26}$$ $$\mathstrut +\mathstrut 6q^{27}$$ $$\mathstrut -\mathstrut 33q^{28}$$ $$\mathstrut -\mathstrut 18q^{29}$$ $$\mathstrut +\mathstrut 30q^{30}$$ $$\mathstrut -\mathstrut 10q^{31}$$ $$\mathstrut +\mathstrut 39q^{32}$$ $$\mathstrut +\mathstrut 12q^{33}$$ $$\mathstrut +\mathstrut 12q^{34}$$ $$\mathstrut +\mathstrut 24q^{35}$$ $$\mathstrut +\mathstrut 36q^{36}$$ $$\mathstrut -\mathstrut 14q^{37}$$ $$\mathstrut +\mathstrut 54q^{38}$$ $$\mathstrut +\mathstrut 24q^{39}$$ $$\mathstrut +\mathstrut 48q^{40}$$ $$\mathstrut +\mathstrut 60q^{41}$$ $$\mathstrut +\mathstrut 54q^{42}$$ $$\mathstrut -\mathstrut 8q^{43}$$ $$\mathstrut +\mathstrut 66q^{44}$$ $$\mathstrut +\mathstrut 36q^{45}$$ $$\mathstrut +\mathstrut 24q^{46}$$ $$\mathstrut +\mathstrut 18q^{47}$$ $$\mathstrut -\mathstrut 24q^{48}$$ $$\mathstrut +\mathstrut 3q^{49}$$ $$\mathstrut -\mathstrut 9q^{50}$$ $$\mathstrut -\mathstrut 12q^{51}$$ $$\mathstrut +\mathstrut 8q^{52}$$ $$\mathstrut -\mathstrut 42q^{53}$$ $$\mathstrut -\mathstrut 42q^{54}$$ $$\mathstrut -\mathstrut 48q^{55}$$ $$\mathstrut -\mathstrut 87q^{56}$$ $$\mathstrut -\mathstrut 72q^{57}$$ $$\mathstrut -\mathstrut 36q^{58}$$ $$\mathstrut -\mathstrut 96q^{59}$$ $$\mathstrut -\mathstrut 114q^{60}$$ $$\mathstrut -\mathstrut 22q^{61}$$ $$\mathstrut -\mathstrut 156q^{62}$$ $$\mathstrut -\mathstrut 96q^{63}$$ $$\mathstrut -\mathstrut 127q^{64}$$ $$\mathstrut -\mathstrut 72q^{65}$$ $$\mathstrut -\mathstrut 54q^{66}$$ $$\mathstrut -\mathstrut 12q^{67}$$ $$\mathstrut -\mathstrut 120q^{68}$$ $$\mathstrut -\mathstrut 36q^{69}$$ $$\mathstrut +\mathstrut 24q^{70}$$ $$\mathstrut -\mathstrut 12q^{71}$$ $$\mathstrut -\mathstrut 66q^{72}$$ $$\mathstrut +\mathstrut 14q^{73}$$ $$\mathstrut +\mathstrut 12q^{74}$$ $$\mathstrut +\mathstrut 38q^{76}$$ $$\mathstrut +\mathstrut 36q^{77}$$ $$\mathstrut +\mathstrut 12q^{78}$$ $$\mathstrut +\mathstrut 36q^{79}$$ $$\mathstrut +\mathstrut 36q^{80}$$ $$\mathstrut +\mathstrut 72q^{81}$$ $$\mathstrut +\mathstrut 18q^{82}$$ $$\mathstrut +\mathstrut 66q^{83}$$ $$\mathstrut +\mathstrut 132q^{84}$$ $$\mathstrut +\mathstrut 24q^{85}$$ $$\mathstrut +\mathstrut 126q^{86}$$ $$\mathstrut +\mathstrut 78q^{87}$$ $$\mathstrut +\mathstrut 78q^{88}$$ $$\mathstrut +\mathstrut 132q^{89}$$ $$\mathstrut +\mathstrut 150q^{90}$$ $$\mathstrut +\mathstrut 38q^{91}$$ $$\mathstrut +\mathstrut 132q^{92}$$ $$\mathstrut +\mathstrut 102q^{93}$$ $$\mathstrut +\mathstrut 90q^{94}$$ $$\mathstrut +\mathstrut 114q^{95}$$ $$\mathstrut +\mathstrut 168q^{96}$$ $$\mathstrut +\mathstrut 56q^{97}$$ $$\mathstrut +\mathstrut 123q^{98}$$ $$\mathstrut +\mathstrut 72q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$

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
63.2.a $$\chi_{63}(1, \cdot)$$ 63.2.a.a 1 1
63.2.a.b 2
63.2.c $$\chi_{63}(62, \cdot)$$ 63.2.c.a 4 1
63.2.e $$\chi_{63}(37, \cdot)$$ 63.2.e.a 2 2
63.2.e.b 2
63.2.f $$\chi_{63}(22, \cdot)$$ 63.2.f.a 6 2
63.2.f.b 6
63.2.g $$\chi_{63}(4, \cdot)$$ 63.2.g.a 2 2
63.2.g.b 10
63.2.h $$\chi_{63}(25, \cdot)$$ 63.2.h.a 2 2
63.2.h.b 10
63.2.i $$\chi_{63}(5, \cdot)$$ 63.2.i.a 2 2
63.2.i.b 10
63.2.o $$\chi_{63}(20, \cdot)$$ 63.2.o.a 12 2
63.2.p $$\chi_{63}(17, \cdot)$$ 63.2.p.a 4 2
63.2.s $$\chi_{63}(47, \cdot)$$ 63.2.s.a 2 2
63.2.s.b 10

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(63))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(63)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 2}$$