# Properties

 Label 200.4.c Level $200$ Weight $4$ Character orbit 200.c Rep. character $\chi_{200}(49,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $7$ Sturm bound $120$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$200 = 2^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 200.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$120$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(200, [\chi])$$.

Total New Old
Modular forms 102 14 88
Cusp forms 78 14 64
Eisenstein series 24 0 24

## Trace form

 $$14 q - 172 q^{9} + O(q^{10})$$ $$14 q - 172 q^{9} - 94 q^{11} + 46 q^{19} + 460 q^{21} - 368 q^{29} - 492 q^{31} - 40 q^{39} + 1246 q^{41} - 1254 q^{49} - 1230 q^{51} + 704 q^{59} + 572 q^{61} + 700 q^{69} - 2520 q^{71} + 500 q^{79} + 3646 q^{81} + 966 q^{89} - 2368 q^{91} + 7412 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(200, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.4.c.a $2$ $11.800$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+5iq^{3}+9iq^{7}-73q^{9}-2^{4}q^{11}+\cdots$$
200.4.c.b $2$ $11.800$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+9iq^{3}-26iq^{7}-54q^{9}-59q^{11}+\cdots$$
200.4.c.c $2$ $11.800$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}-17iq^{7}-9q^{9}+2^{4}q^{11}+\cdots$$
200.4.c.d $2$ $11.800$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+5iq^{3}-2iq^{7}+2q^{9}+39q^{11}+\cdots$$
200.4.c.e $2$ $11.800$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+12iq^{7}+11q^{9}-44q^{11}+\cdots$$
200.4.c.f $2$ $11.800$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}-8iq^{7}+11q^{9}+6^{2}q^{11}+\cdots$$
200.4.c.g $2$ $11.800$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+6iq^{7}+26q^{9}-19q^{11}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(200, [\chi])$$ into lower level spaces

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