# Properties

 Label 380.2.l Level $380$ Weight $2$ Character orbit 380.l Rep. character $\chi_{380}(37,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $20$ 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.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(i)$$ 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 132 20 112
Cusp forms 108 20 88
Eisenstein series 24 0 24

## Trace form

 $$20 q + 2 q^{5} - 2 q^{7} + O(q^{10})$$ $$20 q + 2 q^{5} - 2 q^{7} + 8 q^{11} + 10 q^{17} + 20 q^{23} + 14 q^{25} + 14 q^{35} - 26 q^{43} - 40 q^{45} - 6 q^{47} - 16 q^{55} + 24 q^{57} + 16 q^{61} + 2 q^{63} - 54 q^{73} + 10 q^{77} - 68 q^{81} + 20 q^{83} - 52 q^{85} - 80 q^{87} + 8 q^{93} + 22 q^{95} + O(q^{100})$$

## 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.l.a $8$ $3.034$ 8.0.2702336256.1 $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$-2$$ $$-6$$ $$q+\beta _{6}q^{5}+(-1+\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots$$
380.2.l.b $12$ $3.034$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$4$$ $$4$$ $$q-\beta _{2}q^{3}+(\beta _{3}-\beta _{8})q^{5}+\beta _{6}q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(380, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(380, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$