# Properties

 Label 2550.2.d Level $2550$ Weight $2$ Character orbit 2550.d Rep. character $\chi_{2550}(2449,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $22$ Sturm bound $1080$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2550.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$22$$ Sturm bound: $$1080$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2550, [\chi])$$.

Total New Old
Modular forms 564 48 516
Cusp forms 516 48 468
Eisenstein series 48 0 48

## Trace form

 $$48 q - 48 q^{4} + 4 q^{6} - 48 q^{9} + O(q^{10})$$ $$48 q - 48 q^{4} + 4 q^{6} - 48 q^{9} - 16 q^{11} + 16 q^{14} + 48 q^{16} + 8 q^{21} - 4 q^{24} - 16 q^{26} - 32 q^{29} + 16 q^{31} - 8 q^{34} + 48 q^{36} - 8 q^{39} + 32 q^{41} + 16 q^{44} - 48 q^{49} + 4 q^{51} - 4 q^{54} - 16 q^{56} - 16 q^{59} - 48 q^{64} - 8 q^{69} + 16 q^{74} - 16 q^{79} + 48 q^{81} - 8 q^{84} + 32 q^{86} + 64 q^{89} + 48 q^{91} + 32 q^{94} + 4 q^{96} + 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2550, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2550.2.d.a $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots$$
2550.2.d.b $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$$
2550.2.d.c $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$$
2550.2.d.d $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$$
2550.2.d.e $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$$
2550.2.d.f $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
2550.2.d.g $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
2550.2.d.h $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$$
2550.2.d.i $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$$
2550.2.d.j $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
2550.2.d.k $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots$$
2550.2.d.l $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots$$
2550.2.d.m $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots$$
2550.2.d.n $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$$
2550.2.d.o $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots$$
2550.2.d.p $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+5iq^{7}+\cdots$$
2550.2.d.q $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$$
2550.2.d.r $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$$
2550.2.d.s $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots$$
2550.2.d.t $2$ $20.362$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots$$
2550.2.d.u $4$ $20.362$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+q^{6}+\beta _{2}q^{7}+\cdots$$
2550.2.d.v $4$ $20.362$ $$\Q(i, \sqrt{33})$$ 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 $$S_{2}^{\mathrm{old}}(2550, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2550, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(85, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(170, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(255, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(425, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(510, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(850, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1275, [\chi])$$$$^{\oplus 2}$$