# Properties

 Label 361.2.c Level $361$ Weight $2$ Character orbit 361.c Rep. character $\chi_{361}(68,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $42$ Newform subspaces $10$ Sturm bound $63$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$361 = 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 361.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$10$$ Sturm bound: $$63$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(361, [\chi])$$.

Total New Old
Modular forms 82 74 8
Cusp forms 42 42 0
Eisenstein series 40 32 8

## Trace form

 $$42 q - 12 q^{4} - q^{5} + 2 q^{7} - 3 q^{9} + O(q^{10})$$ $$42 q - 12 q^{4} - q^{5} + 2 q^{7} - 3 q^{9} + 2 q^{11} + 6 q^{16} - q^{17} - 28 q^{20} - 4 q^{23} - 8 q^{24} + 14 q^{25} + 16 q^{26} - 4 q^{28} + 16 q^{30} - 5 q^{35} + 16 q^{36} - 24 q^{39} + 30 q^{42} - 5 q^{43} - 12 q^{44} + 10 q^{45} - 7 q^{47} - 56 q^{49} - 14 q^{54} - 9 q^{55} - 28 q^{58} - 5 q^{61} - 6 q^{62} - 11 q^{63} - 72 q^{64} + 42 q^{66} + 20 q^{68} - 9 q^{73} - 12 q^{74} - 14 q^{77} + 18 q^{80} + 47 q^{81} - 10 q^{82} + 16 q^{83} - 15 q^{85} + 20 q^{87} + 56 q^{92} - 8 q^{93} + 12 q^{96} - 21 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(361, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
361.2.c.a $2$ $2.883$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-3$$ $$-2$$ $$q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$$
361.2.c.b $2$ $2.883$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$1$$ $$6$$ $$q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+3q^{7}+3\zeta_{6}q^{9}+\cdots$$
361.2.c.c $2$ $2.883$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$-3$$ $$-2$$ $$q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$$
361.2.c.d $4$ $2.883$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$-1$$ $$-3$$ $$-2$$ $$12$$ $$q-\beta _{1}q^{2}+(-2+\beta _{1}-2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$$
361.2.c.e $4$ $2.883$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$0$$ $$-4$$ $$-1$$ $$-4$$ $$q+(1-2\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{3})q^{3}+\cdots$$
361.2.c.f $4$ $2.883$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$0$$ $$4$$ $$-1$$ $$-4$$ $$q+(1-2\beta _{1}+\beta _{3})q^{2}+(2+2\beta _{3})q^{3}+\cdots$$
361.2.c.g $4$ $2.883$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$1$$ $$3$$ $$-2$$ $$12$$ $$q+\beta _{1}q^{2}+(2-\beta _{1}+2\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
361.2.c.h $6$ $2.883$ $$\Q(\zeta_{18})$$ None $$-3$$ $$-3$$ $$3$$ $$0$$ $$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-1+\zeta_{18}+\cdots)q^{3}+\cdots$$
361.2.c.i $6$ $2.883$ $$\Q(\zeta_{18})$$ None $$3$$ $$3$$ $$3$$ $$0$$ $$q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$$
361.2.c.j $8$ $2.883$ 8.0.324000000.2 None $$0$$ $$0$$ $$4$$ $$-16$$ $$q+\beta _{3}q^{2}-\beta _{3}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots$$