# Properties

 Label 429.2.bg Level $429$ Weight $2$ Character orbit 429.bg Rep. character $\chi_{429}(16,\cdot)$ Character field $\Q(\zeta_{15})$ 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.bg (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{15})$$ 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

 $$224q + 28q^{4} + 28q^{9} + O(q^{10})$$ $$224q + 28q^{4} + 28q^{9} - 24q^{10} + 4q^{11} - 16q^{12} - 14q^{13} - 24q^{14} - 4q^{15} + 8q^{16} - 16q^{17} - 68q^{20} + 22q^{22} + 12q^{23} - 36q^{24} - 68q^{25} + 56q^{26} - 12q^{28} - 12q^{29} - 4q^{30} + 8q^{31} - 40q^{32} - 2q^{33} + 160q^{34} - 20q^{35} + 28q^{36} + 24q^{37} - 68q^{38} + 8q^{39} - 56q^{40} - 76q^{41} - 12q^{42} - 32q^{43} + 60q^{46} + 68q^{47} - 40q^{48} + 80q^{49} - 20q^{50} - 8q^{51} - 58q^{52} - 100q^{53} + 12q^{55} + 8q^{58} + 2q^{59} - 24q^{60} + 36q^{61} - 16q^{62} - 20q^{65} - 24q^{66} - 88q^{67} - 52q^{68} + 14q^{69} + 128q^{70} - 32q^{71} - 84q^{73} - 68q^{74} - 32q^{75} + 32q^{76} + 116q^{77} - 16q^{78} - 88q^{79} + 64q^{80} + 28q^{81} + 10q^{82} - 16q^{83} + 20q^{85} - 96q^{86} - 112q^{87} - 92q^{88} + 24q^{89} + 8q^{90} - 50q^{91} - 4q^{92} - 8q^{93} + 20q^{94} + 36q^{95} - 156q^{96} + 46q^{97} + 80q^{98} + 12q^{99} + O(q^{100})$$

## 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.bg.a $$112$$ $$3.426$$ None $$0$$ $$-14$$ $$6$$ $$0$$
429.2.bg.b $$112$$ $$3.426$$ None $$0$$ $$14$$ $$-6$$ $$0$$

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

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