# Properties

 Label 63.4.c Level $63$ Weight $4$ Character orbit 63.c Rep. character $\chi_{63}(62,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $32$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 63.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(63, [\chi])$$.

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

## Trace form

 $$8q - 32q^{4} - 44q^{7} + O(q^{10})$$ $$8q - 32q^{4} - 44q^{7} + 188q^{16} - 996q^{22} + 776q^{25} + 980q^{28} - 736q^{37} - 760q^{43} + 132q^{46} + 968q^{49} - 1164q^{58} - 5600q^{64} + 4144q^{67} + 3552q^{70} - 2192q^{79} - 5328q^{85} + 6852q^{88} + 1776q^{91} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(63, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
63.4.c.a $$4$$ $$3.717$$ $$\Q(\sqrt{-2}, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-8-5\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots$$
63.4.c.b $$4$$ $$3.717$$ $$\Q(\sqrt{-2}, \sqrt{111})$$ None $$0$$ $$0$$ $$0$$ $$-44$$ $$q+2\beta _{1}q^{2}+\beta _{3}q^{5}+(-11-\beta _{2})q^{7}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(63, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(63, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$