# Properties

 Label 350.2.x Level 350 Weight 2 Character orbit x Rep. character $$\chi_{350}(3,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 320 Newform subspaces 1 Sturm bound 120 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$350 = 2 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 350.x (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$120$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(350, [\chi])$$.

Total New Old
Modular forms 1024 320 704
Cusp forms 896 320 576
Eisenstein series 128 0 128

## Trace form

 $$320q + 12q^{5} - 8q^{7} + O(q^{10})$$ $$320q + 12q^{5} - 8q^{7} + 12q^{10} - 16q^{15} - 40q^{16} + 36q^{17} + 8q^{18} - 72q^{22} + 44q^{23} - 12q^{25} - 24q^{28} - 80q^{29} + 20q^{30} - 48q^{33} - 28q^{35} + 80q^{36} - 4q^{37} - 24q^{38} - 40q^{39} - 36q^{42} + 88q^{43} - 228q^{45} - 12q^{47} + 32q^{50} - 52q^{53} + 152q^{57} + 32q^{58} - 120q^{59} - 8q^{60} + 136q^{63} + 8q^{65} - 32q^{67} - 144q^{68} + 92q^{70} + 8q^{72} + 12q^{73} - 432q^{75} + 144q^{77} - 16q^{78} + 12q^{80} - 40q^{81} - 192q^{82} + 60q^{84} - 24q^{85} + 24q^{87} + 4q^{88} - 300q^{89} - 8q^{92} - 68q^{93} + 20q^{95} - 40q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(350, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
350.2.x.a $$320$$ $$2.795$$ None $$0$$ $$0$$ $$12$$ $$-8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(350, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(350, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database