# Properties

 Label 799.1.c Level $799$ Weight $1$ Character orbit 799.c Rep. character $\chi_{799}(798,\cdot)$ Character field $\Q$ Dimension $11$ Newform subspaces $4$ Sturm bound $72$ Trace bound $2$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 13 13 0
Cusp forms 11 11 0
Eisenstein series 2 2 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 11 0 0 0

## Trace form

 $$11 q + 7 q^{4} + q^{9} + O(q^{10})$$ $$11 q + 7 q^{4} + q^{9} + 3 q^{16} - 2 q^{17} - 10 q^{18} + q^{25} - 10 q^{32} - 3 q^{36} + 10 q^{42} + 3 q^{47} + q^{49} - 8 q^{50} + 5 q^{51} - 4 q^{53} - 4 q^{55} - q^{64} - q^{68} - 10 q^{72} + 11 q^{81} + 6 q^{83} + 10 q^{84} - 4 q^{89} + O(q^{100})$$

## 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.c.a $1$ $0.399$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-47})$$, $$\Q(\sqrt{-799})$$ $$\Q(\sqrt{17})$$ $$-2$$ $$0$$ $$0$$ $$0$$ $$q-2q^{2}+3q^{4}-4q^{8}+q^{9}+5q^{16}+\cdots$$
799.1.c.b $2$ $0.399$ $$\Q(\sqrt{2})$$ $D_{4}$ $$\Q(\sqrt{-799})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-q^{4}-\beta q^{5}+q^{9}+\beta q^{11}+q^{16}+\cdots$$
799.1.c.c $4$ $0.399$ $$\Q(\zeta_{16})^+$$ $D_{8}$ $$\Q(\sqrt{-799})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{3})q^{10}+\cdots$$
799.1.c.d $4$ $0.399$ $$\Q(\zeta_{10})$$ $D_{10}$ $$\Q(\sqrt{-47})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{3}+\cdots$$