# Properties

 Label 63.1.d Level 63 Weight 1 Character orbit d Rep. character $$\chi_{63}(55,\cdot)$$ Character field $$\Q$$ Dimension 1 Newforms 1 Sturm bound 8 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 63.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$7$$ Character field: $$\Q$$ Newforms: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(63, [\chi])$$.

Total New Old
Modular forms 5 2 3
Cusp forms 1 1 0
Eisenstein series 4 1 3

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q$$ $$\mathstrut -\mathstrut q^{4}$$ $$\mathstrut -\mathstrut q^{7}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$q$$ $$\mathstrut -\mathstrut q^{4}$$ $$\mathstrut -\mathstrut q^{7}$$ $$\mathstrut +\mathstrut q^{16}$$ $$\mathstrut +\mathstrut q^{25}$$ $$\mathstrut +\mathstrut q^{28}$$ $$\mathstrut -\mathstrut 2q^{37}$$ $$\mathstrut -\mathstrut 2q^{43}$$ $$\mathstrut +\mathstrut q^{49}$$ $$\mathstrut -\mathstrut q^{64}$$ $$\mathstrut +\mathstrut 2q^{67}$$ $$\mathstrut +\mathstrut 2q^{79}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(63, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
63.1.d.a $$1$$ $$0.031$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{21})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$$