# Properties

 Label 380.2.d Level $380$ Weight $2$ Character orbit 380.d Rep. character $\chi_{380}(379,\cdot)$ Character field $\Q$ Dimension $56$ Newform subspaces $2$ Sturm bound $120$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$380$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$120$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(380, [\chi])$$.

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

## Trace form

 $$56 q - 4 q^{5} + 8 q^{6} - 56 q^{9} + O(q^{10})$$ $$56 q - 4 q^{5} + 8 q^{6} - 56 q^{9} - 8 q^{16} - 20 q^{20} - 32 q^{24} - 4 q^{25} - 16 q^{30} - 32 q^{36} + 32 q^{44} - 12 q^{45} + 16 q^{49} - 32 q^{54} + 24 q^{61} + 72 q^{64} + 8 q^{66} + 32 q^{74} + 56 q^{76} - 24 q^{80} + 72 q^{81} + 44 q^{85} + 96 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(380, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.d.a $16$ $3.034$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{6}q^{5}+\cdots$$
380.2.d.b $40$ $3.034$ None $$0$$ $$0$$ $$-4$$ $$0$$