# Properties

 Label 385.2.o Level $385$ Weight $2$ Character orbit 385.o Rep. character $\chi_{385}(54,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $88$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$385 = 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 385.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$385$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(385, [\chi])$$.

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

## Trace form

 $$88q - 44q^{4} - 36q^{9} + O(q^{10})$$ $$88q - 44q^{4} - 36q^{9} - 4q^{11} - 12q^{14} - 4q^{15} - 40q^{16} - 8q^{25} + 24q^{26} - 36q^{31} + 72q^{36} - 8q^{44} + 30q^{45} + 28q^{49} - 28q^{56} - 36q^{59} + 60q^{66} - 42q^{70} + 32q^{71} - 108q^{75} - 90q^{80} + 20q^{81} + 32q^{86} - 72q^{89} + 128q^{91} + 120q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(385, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
385.2.o.a $$16$$ $$3.074$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ $$\Q(\sqrt{-55})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{10}-\beta _{14})q^{2}+(\beta _{1}+2\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$$
385.2.o.b $$72$$ $$3.074$$ None $$0$$ $$0$$ $$0$$ $$0$$