# Properties

 Label 429.2.p Level $429$ Weight $2$ Character orbit 429.p Rep. character $\chi_{429}(230,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $104$ Newform subspaces $2$ Sturm bound $112$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$429 = 3 \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 429.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$429$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$112$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

## Trace form

 $$104q - 2q^{3} - 52q^{4} + 2q^{9} + O(q^{10})$$ $$104q - 2q^{3} - 52q^{4} + 2q^{9} + 12q^{12} + 8q^{15} - 60q^{16} + 16q^{22} - 80q^{25} + 4q^{27} - 32q^{31} - 4q^{33} - 56q^{34} + 32q^{36} - 4q^{37} - 22q^{42} + 22q^{45} + 8q^{48} + 16q^{49} + 12q^{55} - 16q^{58} - 12q^{60} + 40q^{64} + 68q^{66} + 28q^{67} + 38q^{69} + 88q^{70} - 54q^{75} - 28q^{78} - 38q^{81} + 32q^{82} - 8q^{88} - 28q^{91} + 26q^{93} - 36q^{97} - 116q^{99} + O(q^{100})$$

## 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.p.a $$8$$ $$3.426$$ 8.0.$$\cdots$$.7 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1+\beta _{2}+\beta _{3})q^{3}+2\beta _{2}q^{4}-2\beta _{6}q^{5}+\cdots$$
429.2.p.b $$96$$ $$3.426$$ None $$0$$ $$2$$ $$0$$ $$0$$