# Properties

 Label 429.2.y Level $429$ Weight $2$ Character orbit 429.y Rep. character $\chi_{429}(116,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $208$ 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.y (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$429$$ Character field: $$\Q(\zeta_{10})$$ 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 240 240 0
Cusp forms 208 208 0
Eisenstein series 32 32 0

## Trace form

 $$208q - 6q^{3} + 36q^{4} - 18q^{9} + O(q^{10})$$ $$208q - 6q^{3} + 36q^{4} - 18q^{9} - 12q^{12} - 10q^{13} - 56q^{16} - 68q^{22} - 60q^{25} + 6q^{27} + 80q^{30} - 68q^{36} + 50q^{39} + 60q^{40} + 52q^{42} - 40q^{48} - 32q^{49} - 90q^{51} - 50q^{52} + 12q^{55} + 92q^{64} - 122q^{66} + 96q^{69} + 22q^{75} - 112q^{78} - 60q^{79} - 2q^{81} + 60q^{82} - 188q^{88} + 160q^{90} + 62q^{91} - 180q^{94} + O(q^{100})$$

## 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.y.a $$32$$ $$3.426$$ $$\Q(\sqrt{-39})$$ $$0$$ $$0$$ $$0$$ $$0$$
429.2.y.b $$176$$ $$3.426$$ None $$0$$ $$-6$$ $$0$$ $$0$$