Properties

 Label 429.2.bj Level $429$ Weight $2$ Character orbit 429.bj Rep. character $\chi_{429}(73,\cdot)$ Character field $\Q(\zeta_{20})$ 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.bj (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$143$$ Character field: $$\Q(\zeta_{20})$$ 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

 $$224q - 56q^{9} + O(q^{10})$$ $$224q - 56q^{9} - 24q^{11} + 20q^{13} - 48q^{14} + 8q^{15} + 32q^{16} - 76q^{20} + 40q^{22} + 60q^{24} - 8q^{26} - 40q^{29} - 32q^{31} + 4q^{33} - 64q^{34} + 24q^{37} - 120q^{41} + 48q^{42} - 12q^{44} - 40q^{46} - 92q^{47} - 112q^{48} + 100q^{52} + 120q^{53} - 32q^{55} - 32q^{58} - 20q^{59} - 72q^{60} - 40q^{61} + 56q^{66} + 72q^{67} + 120q^{68} - 80q^{70} - 32q^{71} + 60q^{73} - 136q^{78} - 80q^{79} - 48q^{80} - 56q^{81} + 140q^{83} - 80q^{85} + 80q^{86} - 48q^{89} - 48q^{91} - 64q^{92} + 16q^{93} - 40q^{94} + 100q^{96} + 100q^{97} - 4q^{99} + O(q^{100})$$

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.bj.a $$112$$ $$3.426$$ None $$0$$ $$-28$$ $$-6$$ $$0$$
429.2.bj.b $$112$$ $$3.426$$ None $$0$$ $$28$$ $$6$$ $$0$$

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

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