# Properties

 Label 385.2.j Level $385$ Weight $2$ Character orbit 385.j Rep. character $\chi_{385}(188,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $80$ Newform subspaces $4$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$385 = 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 385.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

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

Total New Old
Modular forms 104 80 24
Cusp forms 88 80 8
Eisenstein series 16 0 16

## Trace form

 $$80q + 24q^{8} + O(q^{10})$$ $$80q + 24q^{8} - 24q^{15} - 96q^{16} + 16q^{18} + 32q^{21} + 8q^{23} - 20q^{28} + 88q^{30} + 8q^{32} - 60q^{35} - 32q^{36} - 16q^{42} - 24q^{43} - 48q^{46} - 112q^{50} + 24q^{53} - 24q^{57} + 72q^{58} + 72q^{60} + 20q^{63} - 48q^{65} - 16q^{67} + 48q^{70} + 32q^{71} + 128q^{72} + 96q^{78} - 144q^{81} - 48q^{85} - 128q^{86} - 24q^{88} - 80q^{91} + 88q^{92} - 40q^{93} - 80q^{95} + 96q^{98} + O(q^{100})$$

## 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.j.a $$4$$ $$3.074$$ $$\Q(\zeta_{12})$$ None $$-4$$ $$-6$$ $$-2$$ $$-8$$ $$q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
385.2.j.b $$4$$ $$3.074$$ $$\Q(\zeta_{12})$$ None $$-4$$ $$6$$ $$2$$ $$0$$ $$q+(-1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
385.2.j.c $$32$$ $$3.074$$ None $$8$$ $$0$$ $$0$$ $$8$$
385.2.j.d $$40$$ $$3.074$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(385, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(385, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$