# Properties

 Label 450.2.c Level $450$ Weight $2$ Character orbit 450.c Rep. character $\chi_{450}(199,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $4$ Sturm bound $180$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$450 = 2 \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 450.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$180$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(450, [\chi])$$.

Total New Old
Modular forms 114 8 106
Cusp forms 66 8 58
Eisenstein series 48 0 48

## Trace form

 $$8 q - 8 q^{4} + O(q^{10})$$ $$8 q - 8 q^{4} + 6 q^{11} + 4 q^{14} + 8 q^{16} + 14 q^{19} - 4 q^{26} - 12 q^{29} + 4 q^{31} - 18 q^{34} + 18 q^{41} - 6 q^{44} - 12 q^{46} - 4 q^{56} - 8 q^{61} - 8 q^{64} - 24 q^{71} - 8 q^{74} - 14 q^{76} + 20 q^{79} - 16 q^{86} + 66 q^{89} - 64 q^{91} + 24 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(450, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
450.2.c.a $2$ $3.593$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-6q^{11}+\cdots$$
450.2.c.b $2$ $3.593$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-4iq^{7}-iq^{8}-2iq^{13}+\cdots$$
450.2.c.c $2$ $3.593$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{11}+\cdots$$
450.2.c.d $2$ $3.593$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-2iq^{7}-iq^{8}+6q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(450, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(450, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$