# Properties

 Label 228.2.f Level $228$ Weight $2$ Character orbit 228.f Rep. character $\chi_{228}(151,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $2$ Sturm bound $80$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$228 = 2^{2} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 228.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$80$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(228, [\chi])$$.

Total New Old
Modular forms 44 20 24
Cusp forms 36 20 16
Eisenstein series 8 0 8

## Trace form

 $$20q + 4q^{4} - 4q^{6} + 20q^{9} + O(q^{10})$$ $$20q + 4q^{4} - 4q^{6} + 20q^{9} + 4q^{16} - 32q^{20} - 4q^{24} + 20q^{25} - 32q^{28} + 4q^{36} - 8q^{38} - 48q^{44} - 12q^{49} - 4q^{54} - 12q^{57} + 40q^{58} - 56q^{61} - 16q^{62} + 4q^{64} + 40q^{66} - 32q^{68} - 24q^{73} + 36q^{76} - 8q^{77} + 88q^{80} + 20q^{81} + 24q^{82} - 40q^{85} + 72q^{92} - 24q^{93} - 4q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(228, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
228.2.f.a $$10$$ $$1.821$$ 10.0.$$\cdots$$.1 None $$-2$$ $$10$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots$$
228.2.f.b $$10$$ $$1.821$$ 10.0.$$\cdots$$.1 None $$2$$ $$-10$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(228, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(228, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 2}$$