# Properties

 Label 722.2.c Level $722$ Weight $2$ Character orbit 722.c Rep. character $\chi_{722}(429,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $54$ Newform subspaces $14$ Sturm bound $190$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$722 = 2 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 722.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$190$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(722, [\chi])$$.

Total New Old
Modular forms 230 54 176
Cusp forms 150 54 96
Eisenstein series 80 0 80

## Trace form

 $$54 q + q^{2} + q^{3} - 27 q^{4} + 4 q^{5} - q^{6} - 2 q^{8} - 24 q^{9} + O(q^{10})$$ $$54 q + q^{2} + q^{3} - 27 q^{4} + 4 q^{5} - q^{6} - 2 q^{8} - 24 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 6 q^{13} + 6 q^{14} - 14 q^{15} - 27 q^{16} - 4 q^{17} - 20 q^{18} - 8 q^{20} + 10 q^{21} - 7 q^{22} - 2 q^{23} - q^{24} - 27 q^{25} - 4 q^{26} + 10 q^{27} - 2 q^{29} + 28 q^{30} + 8 q^{31} + q^{32} - 11 q^{33} + 6 q^{34} - 8 q^{35} - 24 q^{36} + 8 q^{37} - 16 q^{39} + 2 q^{40} + 19 q^{41} + 24 q^{42} + 18 q^{43} + q^{44} - 36 q^{45} - 16 q^{46} + 22 q^{47} + q^{48} + 18 q^{49} - 22 q^{50} - 6 q^{51} + 6 q^{52} + 2 q^{53} + 11 q^{54} + 22 q^{55} - 12 q^{56} - 4 q^{58} - 9 q^{59} - 14 q^{60} - 12 q^{61} - 8 q^{62} + 32 q^{63} + 54 q^{64} - 8 q^{65} - 13 q^{66} - 11 q^{67} + 8 q^{68} + 40 q^{69} - 12 q^{70} - 22 q^{71} + 10 q^{72} + 27 q^{73} + 22 q^{74} + 66 q^{75} + 52 q^{77} - 2 q^{78} - 12 q^{79} + 4 q^{80} - 31 q^{81} + 5 q^{82} - 26 q^{83} - 20 q^{84} + 12 q^{85} + 16 q^{86} - 56 q^{87} + 14 q^{88} + 6 q^{89} + 8 q^{90} - 4 q^{91} - 2 q^{92} - 28 q^{94} + 2 q^{96} - q^{97} - 7 q^{98} - 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(722, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
722.2.c.a $2$ $5.765$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$-2$$ $$-6$$ $$q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.b $2$ $5.765$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-8$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.c $2$ $5.765$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.d $2$ $5.765$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$4$$ $$6$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.e $2$ $5.765$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.f $2$ $5.765$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$4$$ $$6$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.g $2$ $5.765$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$-2$$ $$-6$$ $$q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
722.2.c.h $4$ $5.765$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$-2$$ $$2$$ $$5$$ $$-4$$ $$q+(-1-\beta _{3})q^{2}+2\beta _{1}q^{3}+\beta _{3}q^{4}+\cdots$$
722.2.c.i $4$ $5.765$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$2$$ $$-2$$ $$5$$ $$-4$$ $$q+(1+\beta _{3})q^{2}-2\beta _{1}q^{3}+\beta _{3}q^{4}+(3+\cdots)q^{5}+\cdots$$
722.2.c.j $4$ $5.765$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$2$$ $$0$$ $$-2$$ $$4$$ $$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
722.2.c.k $6$ $5.765$ $$\Q(\zeta_{18})$$ None $$-3$$ $$0$$ $$-6$$ $$12$$ $$q+(-1+\zeta_{18})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+\cdots$$
722.2.c.l $6$ $5.765$ $$\Q(\zeta_{18})$$ None $$3$$ $$0$$ $$-6$$ $$12$$ $$q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$$
722.2.c.m $8$ $5.765$ 8.0.324000000.2 None $$-4$$ $$-2$$ $$2$$ $$-4$$ $$q+(-1-\beta _{4})q^{2}+(\beta _{3}+\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots$$
722.2.c.n $8$ $5.765$ 8.0.324000000.2 None $$4$$ $$2$$ $$2$$ $$-4$$ $$q+(1+\beta _{4})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(722, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(722, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(361, [\chi])$$$$^{\oplus 2}$$