# Properties

 Label 798.2.j Level $798$ Weight $2$ Character orbit 798.j Rep. character $\chi_{798}(457,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $48$ Newform subspaces $12$ Sturm bound $320$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$798 = 2 \cdot 3 \cdot 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 798.j (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$320$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(798, [\chi])$$.

Total New Old
Modular forms 336 48 288
Cusp forms 304 48 256
Eisenstein series 32 0 32

## Trace form

 $$48 q - 24 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 24 q^{9} + O(q^{10})$$ $$48 q - 24 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 24 q^{9} + 4 q^{10} + 4 q^{11} - 8 q^{15} - 24 q^{16} - 8 q^{17} - 4 q^{19} - 8 q^{20} - 8 q^{22} + 4 q^{23} - 4 q^{24} - 16 q^{25} + 4 q^{28} - 32 q^{29} + 20 q^{31} + 4 q^{33} + 36 q^{35} + 48 q^{36} + 24 q^{37} + 4 q^{40} + 16 q^{41} - 4 q^{42} + 8 q^{43} + 4 q^{44} + 4 q^{45} - 8 q^{46} - 28 q^{47} - 8 q^{49} + 64 q^{50} + 8 q^{51} - 16 q^{53} - 4 q^{54} - 64 q^{55} - 36 q^{58} - 16 q^{59} + 4 q^{60} - 52 q^{61} - 48 q^{62} + 4 q^{63} + 48 q^{64} + 16 q^{65} - 16 q^{66} + 24 q^{67} - 8 q^{68} - 32 q^{69} + 36 q^{70} - 80 q^{71} + 4 q^{73} - 16 q^{74} + 16 q^{75} + 8 q^{76} + 32 q^{77} + 16 q^{78} + 20 q^{79} + 4 q^{80} - 24 q^{81} + 16 q^{82} + 56 q^{83} - 32 q^{85} + 40 q^{86} + 28 q^{87} + 4 q^{88} + 32 q^{89} - 8 q^{90} + 48 q^{91} - 8 q^{92} + 4 q^{95} - 4 q^{96} + 40 q^{97} + 16 q^{98} - 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(798, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
798.2.j.a $2$ $6.372$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$-1$$ $$1$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
798.2.j.b $2$ $6.372$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-1$$ $$-5$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
798.2.j.c $2$ $6.372$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-1$$ $$-1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
798.2.j.d $2$ $6.372$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-1$$ $$5$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
798.2.j.e $2$ $6.372$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$1$$ $$1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
798.2.j.f $2$ $6.372$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$3$$ $$-1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
798.2.j.g $4$ $6.372$ $$\Q(\zeta_{12})$$ None $$-2$$ $$2$$ $$-4$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+(1-\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
798.2.j.h $4$ $6.372$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$2$$ $$6$$ $$-2$$ $$q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots$$
798.2.j.i $6$ $6.372$ 6.0.4406832.1 None $$-3$$ $$-3$$ $$5$$ $$-1$$ $$q-\beta _{4}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$$
798.2.j.j $6$ $6.372$ 6.0.4406832.1 None $$3$$ $$3$$ $$-1$$ $$-1$$ $$q+\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots$$
798.2.j.k $8$ $6.372$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-4$$ $$-4$$ $$-2$$ $$-2$$ $$q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
798.2.j.l $8$ $6.372$ 8.0.856615824.2 None $$4$$ $$4$$ $$0$$ $$-2$$ $$q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(798, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(798, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(133, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(266, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(399, [\chi])$$$$^{\oplus 2}$$