# Properties

 Label 550.2.b Level $550$ Weight $2$ Character orbit 550.b Rep. character $\chi_{550}(199,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $6$ Sturm bound $180$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$550 = 2 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 550.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$180$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(550, [\chi])$$.

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

## Trace form

 $$14 q - 14 q^{4} + 8 q^{6} - 14 q^{9} + O(q^{10})$$ $$14 q - 14 q^{4} + 8 q^{6} - 14 q^{9} - 2 q^{11} + 14 q^{16} + 8 q^{19} - 16 q^{21} - 8 q^{24} - 24 q^{26} + 4 q^{29} - 4 q^{31} + 28 q^{34} + 14 q^{36} - 8 q^{39} + 44 q^{41} + 2 q^{44} + 24 q^{46} - 38 q^{49} - 32 q^{51} - 32 q^{54} - 32 q^{59} + 12 q^{61} - 14 q^{64} - 8 q^{66} + 48 q^{69} + 4 q^{71} + 12 q^{74} - 8 q^{76} + 24 q^{79} + 14 q^{81} + 16 q^{84} + 4 q^{86} + 24 q^{89} - 56 q^{91} + 8 q^{94} + 8 q^{96} + 26 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(550, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
550.2.b.a $2$ $4.392$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots$$
550.2.b.b $2$ $4.392$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-5iq^{7}+\cdots$$
550.2.b.c $2$ $4.392$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{7}-iq^{8}+\cdots$$
550.2.b.d $2$ $4.392$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+4iq^{7}+\cdots$$
550.2.b.e $2$ $4.392$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{8}+\cdots$$
550.2.b.f $4$ $4.392$ $$\Q(i, \sqrt{33})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+\beta _{3}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(550, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(550, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 2}$$