# Properties

 Label 63.3.d Level $63$ Weight $3$ Character orbit 63.d Rep. character $\chi_{63}(55,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $3$ Sturm bound $24$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 63.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$24$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(63, [\chi])$$.

Total New Old
Modular forms 20 7 13
Cusp forms 12 5 7
Eisenstein series 8 2 6

## Trace form

 $$5 q + q^{2} + 5 q^{4} + 9 q^{7} + 17 q^{8} + O(q^{10})$$ $$5 q + q^{2} + 5 q^{4} + 9 q^{7} + 17 q^{8} - 14 q^{11} - 23 q^{14} - 39 q^{16} - 74 q^{22} + 10 q^{23} + 29 q^{25} + q^{28} + 130 q^{29} - 111 q^{32} - 96 q^{35} + 90 q^{37} - 6 q^{43} + 90 q^{44} + 142 q^{46} + 53 q^{49} + 121 q^{50} - 14 q^{53} - 7 q^{56} - 26 q^{58} - 123 q^{64} - 96 q^{65} - 206 q^{67} + 96 q^{70} + 10 q^{71} - 166 q^{74} - 62 q^{77} - 374 q^{79} + 122 q^{86} - 10 q^{88} - 96 q^{91} - 174 q^{92} + 288 q^{95} + 241 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(63, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.3.d.a $1$ $1.717$ $$\Q$$ $$\Q(\sqrt{-7})$$ $$3$$ $$0$$ $$0$$ $$-7$$ $$q+3q^{2}+5q^{4}-7q^{7}+3q^{8}+6q^{11}+\cdots$$
63.3.d.b $2$ $1.717$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$2$$ $$q-q^{2}-3q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$$
63.3.d.c $2$ $1.717$ $$\Q(\sqrt{7})$$ $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$14$$ $$q+\beta q^{2}+3q^{4}+7q^{7}-\beta q^{8}-8\beta q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(63, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(63, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$