Properties

 Label 760.2.bp Level $760$ Weight $2$ Character orbit 760.bp Rep. character $\chi_{760}(293,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $464$ Newform subspaces $1$ Sturm bound $240$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$760 = 2^{3} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 760.bp (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$760$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$240$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(760, [\chi])$$.

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

 $$464q - 6q^{2} - 16q^{7} + O(q^{10})$$ $$464q - 6q^{2} - 16q^{7} - 6q^{10} - 12q^{15} - 4q^{17} - 32q^{20} + 6q^{22} - 4q^{23} - 4q^{25} + 16q^{26} - 28q^{30} + 24q^{32} + 24q^{33} - 36q^{36} + 22q^{38} - 36q^{40} - 24q^{41} - 18q^{42} - 28q^{47} - 48q^{48} - 6q^{52} + 16q^{55} - 20q^{57} + 52q^{58} - 6q^{60} - 8q^{62} + 48q^{63} - 44q^{66} - 52q^{68} - 6q^{70} - 24q^{71} - 144q^{72} - 4q^{73} + 84q^{76} + 96q^{78} - 42q^{80} + 160q^{81} - 20q^{82} - 120q^{86} - 152q^{87} - 96q^{90} - 8q^{92} + 36q^{95} + 176q^{96} - 12q^{97} + 48q^{98} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(760, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
760.2.bp.a $$464$$ $$6.069$$ None $$-6$$ $$0$$ $$0$$ $$-16$$