# Properties

 Label 760.2.p Level $760$ Weight $2$ Character orbit 760.p Rep. character $\chi_{760}(379,\cdot)$ Character field $\Q$ Dimension $116$ Newform subspaces $9$ Sturm bound $240$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$760 = 2^{3} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 760.p (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$760$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$240$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$29$$

## Dimensions

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

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

## Trace form

 $$116q - 8q^{4} - 16q^{6} + 100q^{9} + O(q^{10})$$ $$116q - 8q^{4} - 16q^{6} + 100q^{9} - 8q^{11} - 8q^{16} + 4q^{19} - 12q^{20} - 4q^{25} + 16q^{26} - 8q^{30} - 40q^{36} + 16q^{44} + 84q^{49} - 56q^{54} - 56q^{64} - 64q^{66} - 40q^{74} - 32q^{80} + 52q^{81} - 16q^{96} - 136q^{99} + O(q^{100})$$

## 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.p.a $$4$$ $$6.069$$ $$\Q(\sqrt{-2}, \sqrt{5})$$ $$\Q(\sqrt{-10})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{5}+2\beta _{3}q^{7}+\cdots$$
760.2.p.b $$4$$ $$6.069$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots$$
760.2.p.c $$4$$ $$6.069$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots$$
760.2.p.d $$8$$ $$6.069$$ 8.0.1499238400.2 None $$-8$$ $$-8$$ $$0$$ $$0$$ $$q+(-1-\beta _{5})q^{2}-q^{3}+2\beta _{5}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$$
760.2.p.e $$8$$ $$6.069$$ 8.0.5473632256.3 None $$-4$$ $$8$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$$
760.2.p.f $$8$$ $$6.069$$ 8.0.5473632256.3 None $$4$$ $$-8$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$$
760.2.p.g $$8$$ $$6.069$$ 8.0.1499238400.2 None $$8$$ $$8$$ $$0$$ $$0$$ $$q+(1+\beta _{5})q^{2}+q^{3}+2\beta _{5}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$$
760.2.p.h $$16$$ $$6.069$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}+\cdots$$
760.2.p.i $$56$$ $$6.069$$ None $$0$$ $$0$$ $$0$$ $$0$$