# Properties

 Label 429.2.bi Level $429$ Weight $2$ Character orbit 429.bi Rep. character $\chi_{429}(5,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $416$ Newform subspaces $1$ Sturm bound $112$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$429 = 3 \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 429.bi (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$429$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$112$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 480 480 0
Cusp forms 416 416 0
Eisenstein series 64 64 0

## Trace form

 $$416q - 12q^{3} - 14q^{6} - 12q^{7} - 12q^{9} + O(q^{10})$$ $$416q - 12q^{3} - 14q^{6} - 12q^{7} - 12q^{9} - 20q^{13} - 30q^{15} + 32q^{16} + 2q^{18} - 4q^{19} - 12q^{21} - 24q^{22} - 78q^{24} - 36q^{27} - 84q^{28} - 28q^{31} - 44q^{33} - 24q^{34} - 12q^{37} + 54q^{39} + 88q^{40} - 56q^{42} + 8q^{45} - 92q^{46} + 40q^{48} - 44q^{52} - 176q^{54} - 72q^{55} - 6q^{57} - 4q^{58} + 12q^{60} - 48q^{61} - 46q^{63} + 204q^{66} - 64q^{67} + 56q^{70} - 66q^{72} - 12q^{73} - 104q^{76} - 92q^{78} + 104q^{79} + 124q^{81} + 16q^{84} - 12q^{85} - 24q^{87} - 84q^{91} - 124q^{93} + 328q^{94} - 152q^{96} + 52q^{97} - 142q^{99} + O(q^{100})$$

## 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.bi.a $$416$$ $$3.426$$ None $$0$$ $$-12$$ $$0$$ $$-12$$