# Properties

 Label 380.2.k Level $380$ Weight $2$ Character orbit 380.k Rep. character $\chi_{380}(267,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $108$ Newform subspaces $4$ Sturm bound $120$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$120$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 128 108 20
Cusp forms 112 108 4
Eisenstein series 16 0 16

## Trace form

 $$108 q + O(q^{10})$$ $$108 q - 16 q^{10} - 16 q^{12} - 4 q^{13} + 16 q^{16} - 20 q^{17} - 16 q^{21} - 16 q^{22} - 20 q^{25} - 32 q^{28} - 24 q^{30} - 40 q^{32} + 16 q^{33} - 16 q^{36} + 20 q^{37} + 24 q^{40} + 20 q^{45} - 48 q^{46} - 20 q^{48} + 4 q^{50} + 20 q^{52} - 44 q^{53} - 8 q^{56} - 32 q^{58} - 20 q^{60} + 24 q^{62} + 20 q^{65} + 72 q^{66} + 8 q^{68} + 76 q^{70} + 100 q^{72} + 36 q^{73} + 24 q^{77} + 24 q^{78} - 96 q^{80} - 28 q^{81} - 24 q^{82} + 4 q^{85} + 32 q^{86} - 20 q^{88} - 16 q^{90} - 40 q^{92} + 48 q^{93} - 40 q^{96} - 60 q^{97} - 64 q^{98} + O(q^{100})$$

## 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.k.a $2$ $3.034$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$-2$$ $$-4$$ $$-4$$ $$q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots$$
380.2.k.b $2$ $3.034$ $$\Q(\sqrt{-1})$$ None $$2$$ $$2$$ $$-4$$ $$4$$ $$q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
380.2.k.c $52$ $3.034$ None $$-2$$ $$-2$$ $$4$$ $$-4$$
380.2.k.d $52$ $3.034$ None $$2$$ $$2$$ $$4$$ $$4$$

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

$$S_{2}^{\mathrm{old}}(380, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 2}$$