Properties

 Label 429.2.bs Level $429$ Weight $2$ Character orbit 429.bs Rep. character $\chi_{429}(7,\cdot)$ Character field $\Q(\zeta_{60})$ Dimension $448$ 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.bs (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{60})$$ 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 960 448 512
Cusp forms 832 448 384
Eisenstein series 128 0 128

Trace form

 $$448q + 56q^{9} + O(q^{10})$$ $$448q + 56q^{9} - 24q^{11} - 20q^{13} + 16q^{15} - 32q^{16} + 28q^{20} + 20q^{22} - 96q^{23} - 60q^{24} + 8q^{26} + 40q^{29} + 8q^{31} - 4q^{33} - 176q^{34} - 24q^{37} + 120q^{41} + 24q^{42} - 48q^{44} - 80q^{46} - 52q^{47} + 16q^{48} - 100q^{52} + 24q^{53} + 20q^{55} - 144q^{56} - 112q^{58} - 184q^{59} + 72q^{60} + 40q^{61} - 80q^{66} - 168q^{67} - 120q^{68} - 64q^{70} + 32q^{71} - 60q^{73} + 136q^{78} + 80q^{79} + 144q^{80} + 56q^{81} - 132q^{82} - 320q^{83} + 80q^{85} - 32q^{86} - 12q^{88} + 192q^{89} + 64q^{92} + 32q^{93} - 80q^{94} - 600q^{95} - 100q^{96} - 28q^{97} + 4q^{99} + O(q^{100})$$

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.bs.a $$224$$ $$3.426$$ None $$0$$ $$-28$$ $$-6$$ $$0$$
429.2.bs.b $$224$$ $$3.426$$ None $$0$$ $$28$$ $$6$$ $$0$$

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

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