# Properties

 Label 2800.2.g Level $2800$ Weight $2$ Character orbit 2800.g Rep. character $\chi_{2800}(449,\cdot)$ Character field $\Q$ Dimension $54$ Newform subspaces $22$ Sturm bound $960$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2800 = 2^{4} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2800.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$22$$ Sturm bound: $$960$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2800, [\chi])$$.

Total New Old
Modular forms 516 54 462
Cusp forms 444 54 390
Eisenstein series 72 0 72

## Trace form

 $$54 q - 54 q^{9} + O(q^{10})$$ $$54 q - 54 q^{9} + 12 q^{11} - 16 q^{19} + 4 q^{29} + 16 q^{31} + 40 q^{39} + 4 q^{41} - 54 q^{49} + 16 q^{51} - 52 q^{61} + 32 q^{69} - 52 q^{71} + 4 q^{79} + 38 q^{81} - 20 q^{89} + 12 q^{91} - 76 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2800, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2800.2.g.a $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}-iq^{7}-6q^{9}+5q^{11}-6iq^{13}+\cdots$$
2800.2.g.b $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}+iq^{7}-6q^{9}+5q^{11}-5iq^{13}+\cdots$$
2800.2.g.c $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}+iq^{7}-6q^{9}+5q^{11}+3iq^{13}+\cdots$$
2800.2.g.d $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}-iq^{7}-q^{9}-5q^{11}+8iq^{17}+\cdots$$
2800.2.g.e $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+iq^{7}-q^{9}-3q^{11}-4iq^{13}+\cdots$$
2800.2.g.f $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots$$
2800.2.g.g $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}-iq^{7}-q^{9}-2iq^{17}-2q^{19}+\cdots$$
2800.2.g.h $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+iq^{7}-q^{9}-4iq^{13}-6iq^{17}+\cdots$$
2800.2.g.i $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-iq^{7}+2q^{9}-3q^{11}-2iq^{13}+\cdots$$
2800.2.g.j $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-iq^{7}+2q^{9}-3q^{11}+iq^{13}+\cdots$$
2800.2.g.k $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}+2q^{9}+q^{11}+6iq^{13}+\cdots$$
2800.2.g.l $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-iq^{7}+2q^{9}+3q^{11}-5iq^{13}+\cdots$$
2800.2.g.m $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-iq^{7}+2q^{9}+5q^{11}+iq^{13}+\cdots$$
2800.2.g.n $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{9}-4q^{11}+6iq^{13}+2iq^{17}+\cdots$$
2800.2.g.o $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{9}-q^{11}-2iq^{13}+4iq^{17}+\cdots$$
2800.2.g.p $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{9}+4q^{11}-2iq^{13}-6iq^{17}+\cdots$$
2800.2.g.q $2$ $22.358$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+3q^{9}+5q^{11}+6iq^{13}+4iq^{17}+\cdots$$
2800.2.g.r $4$ $22.358$ $$\Q(i, \sqrt{33})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-6+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots$$
2800.2.g.s $4$ $22.358$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{7}+(-3+2\beta _{3})q^{9}+\cdots$$
2800.2.g.t $4$ $22.358$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$$
2800.2.g.u $4$ $22.358$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots$$
2800.2.g.v $4$ $22.358$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2800, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2800, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(400, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1400, [\chi])$$$$^{\oplus 2}$$