# Properties

 Label 799.1.e Level $799$ Weight $1$ Character orbit 799.e Rep. character $\chi_{799}(140,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $10$ Newform subspaces $2$ Sturm bound $72$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$799 = 17 \cdot 47$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 799.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$799$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(799, [\chi])$$.

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 10 0 0 0

## Trace form

 $$10 q - 10 q^{4} + O(q^{10})$$ $$10 q - 10 q^{4} - 10 q^{12} - 10 q^{14} + 10 q^{16} + 10 q^{24} - 10 q^{47} + 10 q^{48} + 10 q^{51} + 10 q^{54} + 10 q^{56} - 10 q^{63} - 10 q^{64} - 10 q^{68} - 10 q^{81} + 20 q^{84} - 10 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(799, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
799.1.e.a $2$ $0.399$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-47})$$ None $$0$$ $$2$$ $$0$$ $$-2$$ $$q-iq^{2}+(1-i)q^{3}-3q^{4}+(-2-2i+\cdots)q^{6}+\cdots$$
799.1.e.b $8$ $0.399$ $$\Q(\zeta_{20})$$ $D_{20}$ $$\Q(\sqrt{-47})$$ None $$0$$ $$-2$$ $$0$$ $$2$$ $$q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}+(-\zeta_{20}+\zeta_{20}^{4}+\cdots)q^{3}+\cdots$$