Properties

 Label 735.2.bg Level $735$ Weight $2$ Character orbit 735.bg Rep. character $\chi_{735}(16,\cdot)$ Character field $\Q(\zeta_{21})$ Dimension $456$ Newform subspaces $4$ Sturm bound $224$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 735.bg (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$49$$ Character field: $$\Q(\zeta_{21})$$ Newform subspaces: $$4$$ Sturm bound: $$224$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(735, [\chi])$$.

Total New Old
Modular forms 1392 456 936
Cusp forms 1296 456 840
Eisenstein series 96 0 96

Trace form

 $$456q - 2q^{3} + 40q^{4} - 2q^{7} + 38q^{9} + O(q^{10})$$ $$456q - 2q^{3} + 40q^{4} - 2q^{7} + 38q^{9} - 4q^{10} + 4q^{11} - 4q^{12} + 4q^{13} + 4q^{14} + 52q^{16} + 8q^{17} + 6q^{19} - 16q^{20} + 12q^{21} - 40q^{22} + 96q^{24} + 38q^{25} + 36q^{26} + 4q^{27} + 60q^{28} - 24q^{29} + 6q^{31} + 20q^{32} - 8q^{33} + 72q^{34} + 20q^{35} - 80q^{36} + 76q^{37} - 144q^{38} + 36q^{39} - 12q^{40} - 64q^{41} - 108q^{42} + 12q^{43} - 92q^{44} + 24q^{46} - 104q^{47} - 96q^{48} - 42q^{49} - 52q^{51} - 168q^{52} - 80q^{53} + 24q^{55} - 132q^{56} - 12q^{57} - 76q^{58} - 32q^{59} + 46q^{61} - 136q^{62} + 12q^{63} - 72q^{64} + 12q^{65} + 12q^{66} + 2q^{67} - 12q^{68} - 24q^{69} + 4q^{70} + 48q^{71} + 94q^{73} + 48q^{74} - 2q^{75} - 40q^{76} + 40q^{77} - 24q^{78} + 10q^{79} + 16q^{80} + 38q^{81} - 252q^{82} + 76q^{83} - 48q^{84} - 8q^{85} - 368q^{86} - 24q^{87} + 212q^{88} - 156q^{89} + 8q^{90} - 38q^{91} - 16q^{92} + 6q^{93} - 284q^{94} + 8q^{95} + 192q^{96} - 192q^{97} - 8q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(735, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
735.2.bg.a $$108$$ $$5.869$$ None $$-1$$ $$9$$ $$9$$ $$-13$$
735.2.bg.b $$108$$ $$5.869$$ None $$1$$ $$9$$ $$-9$$ $$9$$
735.2.bg.c $$120$$ $$5.869$$ None $$-1$$ $$-10$$ $$10$$ $$14$$
735.2.bg.d $$120$$ $$5.869$$ None $$1$$ $$-10$$ $$-10$$ $$-12$$

Decomposition of $$S_{2}^{\mathrm{old}}(735, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(735, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 2}$$