# Properties

 Label 429.2.bm Level $429$ Weight $2$ Character orbit 429.bm Rep. character $\chi_{429}(17,\cdot)$ Character field $\Q(\zeta_{30})$ 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.bm (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$429$$ Character field: $$\Q(\zeta_{30})$$ 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

 $$416q - 3q^{3} - 54q^{4} - 15q^{6} - 30q^{7} - 9q^{9} + O(q^{10})$$ $$416q - 3q^{3} - 54q^{4} - 15q^{6} - 30q^{7} - 9q^{9} - 36q^{12} - 20q^{13} - 9q^{15} + 14q^{16} - 30q^{19} - 28q^{22} + 15q^{24} - 84q^{25} - 24q^{27} - 30q^{28} - 5q^{30} - 27q^{33} - 73q^{36} - 18q^{37} - 65q^{39} - 120q^{40} - 25q^{42} + 36q^{45} + 30q^{46} - 41q^{48} + 14q^{49} + 60q^{51} + 20q^{52} + 18q^{55} - 126q^{58} - 30q^{61} + 105q^{63} - 56q^{64} + 170q^{66} - 33q^{69} - 195q^{72} + 77q^{75} + 4q^{78} - 13q^{81} + 36q^{82} - 60q^{84} - 30q^{85} + 38q^{88} - 190q^{90} - 56q^{91} + 24q^{93} - 90q^{94} + 54q^{97} + O(q^{100})$$

## 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.bm.a $$416$$ $$3.426$$ None $$0$$ $$-3$$ $$0$$ $$-30$$