# Properties

 Label 1650.2.c Level $1650$ Weight $2$ Character orbit 1650.c Rep. character $\chi_{1650}(199,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $15$ Sturm bound $720$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1650.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$15$$ Sturm bound: $$720$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$13$$, $$17$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1650, [\chi])$$.

Total New Old
Modular forms 384 32 352
Cusp forms 336 32 304
Eisenstein series 48 0 48

## Trace form

 $$32 q - 32 q^{4} - 32 q^{9} + O(q^{10})$$ $$32 q - 32 q^{4} - 32 q^{9} + 32 q^{16} - 8 q^{19} + 8 q^{21} + 24 q^{26} - 24 q^{29} - 24 q^{31} - 40 q^{34} + 32 q^{36} - 8 q^{39} - 8 q^{41} - 24 q^{49} + 32 q^{59} - 32 q^{64} + 8 q^{66} - 16 q^{69} - 96 q^{71} - 24 q^{74} + 8 q^{76} - 8 q^{79} + 32 q^{81} - 8 q^{84} - 32 q^{86} + 24 q^{89} + 32 q^{91} - 32 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1650, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1650.2.c.a $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$$
1650.2.c.b $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$$
1650.2.c.c $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
1650.2.c.d $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
1650.2.c.e $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$$
1650.2.c.f $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots$$
1650.2.c.g $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots$$
1650.2.c.h $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
1650.2.c.i $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots$$
1650.2.c.j $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots$$
1650.2.c.k $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots$$
1650.2.c.l $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots$$
1650.2.c.m $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$$
1650.2.c.n $2$ $13.175$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$$
1650.2.c.o $4$ $13.175$ $$\Q(i, \sqrt{73})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1650, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1650, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(330, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(550, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(825, [\chi])$$$$^{\oplus 2}$$