# Properties

 Label 429.2.e Level $429$ Weight $2$ Character orbit 429.e Rep. character $\chi_{429}(428,\cdot)$ Character field $\Q$ Dimension $52$ Newform subspaces $4$ Sturm bound $112$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$429 = 3 \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 429.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$429$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$112$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(429, [\chi])$$.

Total New Old
Modular forms 60 60 0
Cusp forms 52 52 0
Eisenstein series 8 8 0

## Trace form

 $$52q - 4q^{3} - 56q^{4} - 12q^{9} + O(q^{10})$$ $$52q - 4q^{3} - 56q^{4} - 12q^{9} - 8q^{12} + 56q^{16} - 12q^{22} + 20q^{25} - 16q^{27} - 22q^{36} - 2q^{42} - 10q^{48} + 12q^{49} + 8q^{55} - 112q^{64} - 18q^{66} - 36q^{69} - 72q^{75} + 62q^{78} + 52q^{81} + 40q^{82} + 28q^{88} + 48q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(429, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
429.2.e.a $$8$$ $$3.426$$ 8.0.$$\cdots$$.21 $$\Q(\sqrt{-39})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-2-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
429.2.e.b $$8$$ $$3.426$$ 8.0.3317760000.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{4}q^{6}+\cdots$$
429.2.e.c $$16$$ $$3.426$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{5}q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$$
429.2.e.d $$20$$ $$3.426$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ $$\Q(\sqrt{-143})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+\beta _{1}q^{3}+(-2+\beta _{8})q^{4}+\beta _{7}q^{6}+\cdots$$