# Properties

 Label 200.3.l Level $200$ Weight $3$ Character orbit 200.l Rep. character $\chi_{200}(57,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $18$ Newform subspaces $6$ Sturm bound $90$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$200 = 2^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 200.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$90$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(200, [\chi])$$.

Total New Old
Modular forms 144 18 126
Cusp forms 96 18 78
Eisenstein series 48 0 48

## Trace form

 $$18 q - 8 q^{7} + O(q^{10})$$ $$18 q - 8 q^{7} + 16 q^{11} + 38 q^{13} + 14 q^{17} - 112 q^{21} - 96 q^{23} - 120 q^{27} + 32 q^{31} + 120 q^{33} + 82 q^{37} + 128 q^{41} - 48 q^{43} + 128 q^{47} + 360 q^{51} + 66 q^{53} + 80 q^{57} - 312 q^{61} - 128 q^{63} - 224 q^{67} - 544 q^{71} - 166 q^{73} - 72 q^{77} - 178 q^{81} + 184 q^{83} + 320 q^{87} - 256 q^{91} - 120 q^{93} - 38 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(200, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.3.l.a $2$ $5.450$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$-14$$ $$q+(-1+i)q^{3}+(-7-7i)q^{7}+7iq^{9}+\cdots$$
200.3.l.b $2$ $5.450$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$6$$ $$q+(-1+i)q^{3}+(3+3i)q^{7}+7iq^{9}+\cdots$$
200.3.l.c $2$ $5.450$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$14$$ $$q+(1-i)q^{3}+(7+7i)q^{7}+7iq^{9}-4q^{11}+\cdots$$
200.3.l.d $4$ $5.450$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$-8$$ $$0$$ $$16$$ $$q+(-2+2\beta _{2}+\beta _{3})q^{3}+(4+4\beta _{1}+4\beta _{2}+\cdots)q^{7}+\cdots$$
200.3.l.e $4$ $5.450$ $$\Q(i, \sqrt{41})$$ None $$0$$ $$2$$ $$0$$ $$-14$$ $$q+(1-\beta _{1}+\beta _{3})q^{3}+(-3-4\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
200.3.l.f $4$ $5.450$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$8$$ $$0$$ $$-16$$ $$q+(2-2\beta _{2}+\beta _{3})q^{3}+(-4+4\beta _{1}-4\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(200, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(200, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$