# Properties

 Label 385.2.bj Level $385$ Weight $2$ Character orbit 385.bj Rep. character $\chi_{385}(8,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $288$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$385 = 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 385.bj (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 416 288 128
Cusp forms 352 288 64
Eisenstein series 64 0 64

## Trace form

 $$288q - 4q^{3} + O(q^{10})$$ $$288q - 4q^{3} + 4q^{11} - 96q^{12} - 16q^{15} + 72q^{16} - 76q^{20} - 44q^{22} - 16q^{23} - 12q^{25} - 64q^{26} - 4q^{27} - 80q^{30} + 32q^{31} - 32q^{33} - 56q^{36} - 4q^{37} - 16q^{38} + 48q^{45} - 40q^{46} + 16q^{47} + 136q^{48} + 80q^{50} - 80q^{51} + 80q^{52} + 76q^{53} + 112q^{55} - 48q^{56} + 80q^{57} + 32q^{58} - 40q^{60} - 220q^{62} + 16q^{66} + 128q^{67} - 16q^{70} - 72q^{71} - 300q^{72} + 48q^{75} - 8q^{77} - 64q^{78} - 80q^{80} + 60q^{81} + 24q^{82} - 200q^{83} - 40q^{85} - 160q^{86} - 352q^{88} - 36q^{91} + 236q^{92} + 68q^{93} + 80q^{95} - 320q^{96} + 44q^{97} + O(q^{100})$$

## 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.bj.a $$288$$ $$3.074$$ None $$0$$ $$-4$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(385, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$