# Properties

 Label 225.2.b Level $225$ Weight $2$ Character orbit 225.b Rep. character $\chi_{225}(199,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $60$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 225.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$60$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(225, [\chi])$$.

Total New Old
Modular forms 42 8 34
Cusp forms 18 6 12
Eisenstein series 24 2 22

## Trace form

 $$6 q + 2 q^{4} + O(q^{10})$$ $$6 q + 2 q^{4} + 4 q^{11} - 12 q^{14} - 2 q^{16} + 4 q^{19} - 8 q^{26} + 16 q^{29} - 20 q^{31} - 4 q^{34} - 4 q^{41} + 16 q^{44} + 24 q^{46} - 26 q^{49} - 28 q^{59} - 16 q^{61} + 18 q^{64} + 32 q^{71} + 28 q^{74} - 24 q^{76} + 8 q^{79} + 4 q^{86} - 12 q^{89} + 44 q^{91} + 8 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(225, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.2.b.a $2$ $1.797$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}+iq^{13}+\cdots$$
225.2.b.b $2$ $1.797$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+3iq^{8}+4q^{11}+2iq^{13}+\cdots$$
225.2.b.c $2$ $1.797$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+iq^{7}-iq^{13}+4q^{16}+q^{19}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(225, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(225, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$