# Properties

 Label 225.2.k Level $225$ Weight $2$ Character orbit 225.k Rep. character $\chi_{225}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $3$ Sturm bound $60$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 225.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$60$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 72 40 32
Cusp forms 48 32 16
Eisenstein series 24 8 16

## Trace form

 $$32 q + 16 q^{4} + 8 q^{6} - 2 q^{9} + O(q^{10})$$ $$32 q + 16 q^{4} + 8 q^{6} - 2 q^{9} + 10 q^{11} - 18 q^{14} - 16 q^{16} + 8 q^{19} - 30 q^{21} + 18 q^{24} - 56 q^{26} - 14 q^{29} - 8 q^{31} + 18 q^{34} + 4 q^{36} - 10 q^{39} + 26 q^{41} - 8 q^{44} - 6 q^{49} - 10 q^{51} - 44 q^{54} + 60 q^{56} + 2 q^{59} + 10 q^{61} - 44 q^{64} - 32 q^{66} - 42 q^{69} - 64 q^{71} + 40 q^{74} - 14 q^{76} - 22 q^{79} - 22 q^{81} + 18 q^{84} + 28 q^{86} + 132 q^{89} - 4 q^{91} - 42 q^{94} + 124 q^{96} + 2 q^{99} + O(q^{100})$$

## 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.k.a $4$ $1.797$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
225.2.k.b $12$ $1.797$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{6}-\beta _{7})q^{2}+\beta _{6}q^{3}+(2+2\beta _{8}+\cdots)q^{4}+\cdots$$
225.2.k.c $16$ $1.797$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{10}+\beta _{14})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$$

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

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