# Properties

 Label 63.3.m Level $63$ Weight $3$ Character orbit 63.m Rep. character $\chi_{63}(10,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $5$ Sturm bound $24$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 63.m (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ 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 40 16 24
Cusp forms 24 12 12
Eisenstein series 16 4 12

## Trace form

 $$12 q + 2 q^{2} - 16 q^{4} + 6 q^{5} - 14 q^{7} - 8 q^{8} + O(q^{10})$$ $$12 q + 2 q^{2} - 16 q^{4} + 6 q^{5} - 14 q^{7} - 8 q^{8} + 48 q^{10} + 14 q^{11} - 22 q^{14} - 52 q^{16} - 48 q^{17} - 78 q^{19} + 80 q^{22} + 68 q^{23} - 6 q^{25} + 126 q^{26} + 172 q^{28} - 64 q^{29} - 66 q^{31} - 12 q^{32} - 114 q^{35} - 46 q^{37} - 174 q^{38} - 348 q^{40} - 28 q^{43} + 108 q^{44} + 104 q^{46} + 222 q^{47} + 186 q^{49} + 68 q^{50} + 492 q^{52} + 32 q^{53} - 32 q^{56} - 148 q^{58} - 84 q^{59} + 180 q^{61} - 152 q^{64} + 78 q^{65} - 126 q^{67} - 36 q^{68} - 588 q^{70} - 244 q^{71} - 150 q^{73} - 38 q^{74} - 52 q^{77} - 54 q^{79} - 48 q^{80} + 324 q^{82} + 528 q^{85} - 158 q^{86} - 332 q^{88} + 60 q^{89} + 258 q^{91} + 168 q^{92} - 204 q^{94} + 150 q^{95} + 176 q^{98} + O(q^{100})$$

## 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.m.a $2$ $1.717$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$6$$ $$-7$$ $$q-2\zeta_{6}q^{2}+(4-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots$$
63.3.m.b $2$ $1.717$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$13$$ $$q+(4-4\zeta_{6})q^{4}+(8-3\zeta_{6})q^{7}+(-7+\cdots)q^{13}+\cdots$$
63.3.m.c $2$ $1.717$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$9$$ $$-7$$ $$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{4}+(6-3\zeta_{6})q^{5}+\cdots$$
63.3.m.d $2$ $1.717$ $$\Q(\sqrt{-3})$$ None $$3$$ $$0$$ $$-9$$ $$13$$ $$q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}+(-6+3\zeta_{6})q^{5}+\cdots$$
63.3.m.e $4$ $1.717$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$-26$$ $$q-\beta _{2}q^{2}+(-9+9\beta _{1})q^{4}+(\beta _{2}+2\beta _{3})q^{5}+\cdots$$

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

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