# Properties

 Label 475.2.v Level $475$ Weight $2$ Character orbit 475.v Rep. character $\chi_{475}(37,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $384$ Newform subspaces $2$ Sturm bound $100$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.v (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$475$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$2$$ Sturm bound: $$100$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(475, [\chi])$$.

Total New Old
Modular forms 416 416 0
Cusp forms 384 384 0
Eisenstein series 32 32 0

## Trace form

 $$384q - 20q^{4} - 18q^{5} - 12q^{6} - 14q^{7} - 20q^{9} + O(q^{10})$$ $$384q - 20q^{4} - 18q^{5} - 12q^{6} - 14q^{7} - 20q^{9} - 12q^{11} + 72q^{16} - 36q^{17} + 10q^{19} - 52q^{20} + 24q^{23} + 2q^{25} - 32q^{26} - 28q^{28} - 60q^{30} + 4q^{35} - 120q^{36} + 16q^{38} - 100q^{39} - 20q^{42} + 58q^{43} - 160q^{44} + 100q^{45} - 82q^{47} - 20q^{54} + 20q^{55} + 70q^{57} - 72q^{58} - 12q^{61} + 72q^{62} - 178q^{63} + 40q^{64} + 36q^{66} + 148q^{68} - 26q^{73} - 32q^{76} - 118q^{77} + 296q^{80} + 52q^{81} - 108q^{82} + 8q^{83} - 100q^{85} + 152q^{87} - 216q^{92} - 164q^{93} + 84q^{95} + 44q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(475, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
475.2.v.a $$16$$ $$3.793$$ 16.0.$$\cdots$$.1 $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$-2$$ $$-6$$ $$q+2\beta _{4}q^{4}+(1-\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots$$
475.2.v.b $$368$$ $$3.793$$ None $$0$$ $$0$$ $$-16$$ $$-8$$