# Properties

 Label 429.2.bn Level $429$ Weight $2$ Character orbit 429.bn Rep. character $\chi_{429}(4,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $224$ Newform subspaces $2$ Sturm bound $112$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$429 = 3 \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 429.bn (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$2$$ Sturm bound: $$112$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 480 224 256
Cusp forms 416 224 192
Eisenstein series 64 0 64

## Trace form

 $$224q - 28q^{4} + 28q^{9} + O(q^{10})$$ $$224q - 28q^{4} + 28q^{9} - 40q^{10} + 36q^{11} + 16q^{12} - 14q^{13} + 24q^{14} - 12q^{15} + 24q^{16} + 8q^{17} - 24q^{19} - 24q^{20} - 26q^{22} + 20q^{23} + 44q^{25} - 48q^{26} + 36q^{28} - 12q^{29} + 20q^{30} + 6q^{33} + 4q^{35} - 28q^{36} + 68q^{38} - 8q^{39} - 40q^{40} + 36q^{41} - 12q^{42} - 96q^{43} + 36q^{46} - 40q^{48} - 80q^{49} + 60q^{50} - 56q^{51} - 2q^{52} - 68q^{53} - 16q^{55} - 176q^{56} + 120q^{58} + 54q^{59} - 12q^{61} + 8q^{62} - 32q^{64} + 52q^{65} - 56q^{66} - 20q^{68} - 14q^{69} + 48q^{71} + 52q^{74} + 32q^{75} - 264q^{76} - 132q^{77} - 40q^{78} + 72q^{79} - 48q^{80} + 28q^{81} + 34q^{82} - 60q^{85} + 112q^{87} + 80q^{88} - 216q^{89} - 40q^{90} - 78q^{91} + 68q^{92} - 24q^{93} - 28q^{94} + 132q^{95} - 162q^{97} + 96q^{98} + O(q^{100})$$

## 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.bn.a $$112$$ $$3.426$$ None $$0$$ $$-14$$ $$0$$ $$0$$
429.2.bn.b $$112$$ $$3.426$$ None $$0$$ $$14$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(429, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(429, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(143, [\chi])$$$$^{\oplus 2}$$