# Properties

 Label 63.2.a Level $63$ Weight $2$ Character orbit 63.a Rep. character $\chi_{63}(1,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $16$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 63.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(63))$$.

Total New Old
Modular forms 12 3 9
Cusp forms 5 3 2
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$3$$$$7$$FrickeDim.
$$+$$$$-$$$$-$$$$2$$
$$-$$$$+$$$$-$$$$1$$
Plus space$$+$$$$0$$
Minus space$$-$$$$3$$

## Trace form

 $$3q + q^{2} + q^{4} + 2q^{5} + q^{7} - 3q^{8} + O(q^{10})$$ $$3q + q^{2} + q^{4} + 2q^{5} + q^{7} - 3q^{8} - 10q^{10} - 4q^{11} + 2q^{13} - q^{14} - 11q^{16} + 6q^{17} - 4q^{19} - 2q^{20} + 8q^{22} + 13q^{25} - 2q^{26} + 3q^{28} + 2q^{29} - 8q^{31} + 5q^{32} + 18q^{34} - 2q^{35} + 10q^{37} + 4q^{38} + 6q^{40} - 2q^{41} - 12q^{43} + 4q^{44} - 12q^{46} + 3q^{49} - q^{50} + 6q^{52} - 6q^{53} - 32q^{55} + 3q^{56} + 2q^{58} - 12q^{59} - 22q^{61} + 9q^{64} - 4q^{65} - 4q^{67} - 6q^{68} - 14q^{70} + 22q^{73} + 6q^{74} - 12q^{76} + 4q^{77} - 2q^{80} + 34q^{82} + 12q^{83} - 12q^{85} - 4q^{86} + 14q^{89} + 6q^{91} + 24q^{94} + 8q^{95} + 46q^{97} + q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(63))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 3 7
63.2.a.a $$1$$ $$0.503$$ $$\Q$$ None $$1$$ $$0$$ $$2$$ $$-1$$ $$-$$ $$+$$ $$q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots$$
63.2.a.b $$2$$ $$0.503$$ $$\Q(\sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$+$$ $$-$$ $$q+\beta q^{2}+q^{4}-2\beta q^{5}+q^{7}-\beta q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(63))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(63)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(21))$$$$^{\oplus 2}$$