# Properties

 Label 735.2.v Level 735 Weight 2 Character orbit v Rep. character $$\chi_{735}(178,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 160 Newform subspaces 4 Sturm bound 224 Trace bound 5

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 735.v (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$4$$ Sturm bound: $$224$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 512 160 352
Cusp forms 384 160 224
Eisenstein series 128 0 128

## Trace form

 $$160q + 12q^{5} + 24q^{8} + O(q^{10})$$ $$160q + 12q^{5} + 24q^{8} + 12q^{10} + 8q^{11} + 8q^{15} + 96q^{16} + 24q^{22} - 20q^{25} - 24q^{26} - 16q^{30} - 24q^{31} - 24q^{32} + 36q^{33} - 160q^{36} + 4q^{37} - 12q^{38} - 12q^{40} - 56q^{43} + 88q^{46} + 60q^{47} - 72q^{50} + 8q^{51} + 108q^{52} - 64q^{53} - 32q^{57} - 108q^{58} - 20q^{60} + 24q^{61} + 20q^{65} - 72q^{66} - 24q^{67} - 132q^{68} - 16q^{71} - 12q^{72} - 36q^{73} - 48q^{75} - 128q^{78} + 12q^{80} + 80q^{81} - 12q^{82} + 88q^{85} + 48q^{86} + 24q^{87} + 32q^{88} + 120q^{92} + 48q^{93} - 4q^{95} + O(q^{100})$$

## 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.v.a $$32$$ $$5.869$$ None $$0$$ $$0$$ $$0$$ $$0$$
735.2.v.b $$32$$ $$5.869$$ None $$0$$ $$0$$ $$12$$ $$0$$
735.2.v.c $$48$$ $$5.869$$ None $$0$$ $$0$$ $$-8$$ $$0$$
735.2.v.d $$48$$ $$5.869$$ None $$0$$ $$0$$ $$8$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(735, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database