# Properties

 Label 349.2.b Level 349 Weight 2 Character orbit b Rep. character $$\chi_{349}(348,\cdot)$$ Character field $$\Q$$ Dimension 28 Newforms 2 Sturm bound 58 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$349$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 349.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$349$$ Character field: $$\Q$$ Newforms: $$2$$ Sturm bound: $$58$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(349, [\chi])$$.

Total New Old
Modular forms 30 30 0
Cusp forms 28 28 0
Eisenstein series 2 2 0

## Trace form

 $$28q - 4q^{3} - 32q^{4} - 8q^{5} + 28q^{9} + O(q^{10})$$ $$28q - 4q^{3} - 32q^{4} - 8q^{5} + 28q^{9} + 8q^{12} + 4q^{14} + 8q^{15} + 28q^{16} - 8q^{17} - 14q^{19} + 6q^{20} - 12q^{22} - 16q^{23} + 16q^{25} + 22q^{26} + 14q^{27} - 16q^{29} + 24q^{31} - 62q^{36} + 24q^{37} + 4q^{41} - 52q^{45} - 82q^{48} - 48q^{49} + 26q^{51} - 38q^{56} - 6q^{57} - 86q^{60} - 80q^{64} + 104q^{66} + 46q^{67} + 48q^{68} - 42q^{69} + 86q^{70} + 50q^{73} - 36q^{75} + 76q^{76} - 68q^{77} - 30q^{78} + 46q^{80} - 4q^{81} - 6q^{83} - 10q^{85} + 60q^{86} + 30q^{87} + 110q^{88} + 28q^{91} + 18q^{92} + 70q^{93} + 22q^{94} - 30q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(349, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
349.2.b.a $$2$$ $$2.787$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-2$$ $$4$$ $$0$$ $$q-q^{3}+2q^{4}+2q^{5}+\beta q^{7}-2q^{9}+\cdots$$
349.2.b.b $$26$$ $$2.787$$ None $$0$$ $$-2$$ $$-12$$ $$0$$