# Properties

 Label 171.3.c Level $171$ Weight $3$ Character orbit 171.c Rep. character $\chi_{171}(37,\cdot)$ Character field $\Q$ Dimension $15$ Newform subspaces $6$ Sturm bound $60$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$171 = 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 171.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$60$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(171, [\chi])$$.

Total New Old
Modular forms 44 17 27
Cusp forms 36 15 21
Eisenstein series 8 2 6

## Trace form

 $$15 q - 22 q^{4} + 3 q^{5} + q^{7} + O(q^{10})$$ $$15 q - 22 q^{4} + 3 q^{5} + q^{7} + 11 q^{11} - 14 q^{16} - 59 q^{17} + 9 q^{19} + 28 q^{20} - 52 q^{23} + 50 q^{25} + 10 q^{26} + 6 q^{28} + 217 q^{35} - 22 q^{38} - 145 q^{43} - 176 q^{44} - 21 q^{47} - 48 q^{49} + 81 q^{55} - 98 q^{58} + 71 q^{61} - 4 q^{62} + 262 q^{64} + 466 q^{68} - 203 q^{73} - 492 q^{74} + 216 q^{76} + 177 q^{77} - 112 q^{80} - 52 q^{82} - 214 q^{83} + 61 q^{85} + 982 q^{92} - 161 q^{95} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(171, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.3.c.a $1$ $4.659$ $$\Q$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$9$$ $$-5$$ $$q+4q^{4}+9q^{5}-5q^{7}-3q^{11}+2^{4}q^{16}+\cdots$$
171.3.c.b $2$ $4.659$ $$\Q(\sqrt{-13})$$ None $$0$$ $$0$$ $$-8$$ $$-10$$ $$q+\beta q^{2}-9q^{4}-4q^{5}-5q^{7}-5\beta q^{8}+\cdots$$
171.3.c.c $2$ $4.659$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-8$$ $$-20$$ $$q-\zeta_{6}q^{2}+q^{4}-4q^{5}-10q^{7}-5\zeta_{6}q^{8}+\cdots$$
171.3.c.d $2$ $4.659$ $$\Q(\sqrt{19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$10$$ $$q+4q^{4}+\beta q^{5}+5q^{7}-5\beta q^{11}+2^{4}q^{16}+\cdots$$
171.3.c.e $4$ $4.659$ $$\Q(\sqrt{-7}, \sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{1}q^{2}-3q^{4}+\beta _{2}q^{5}-2q^{7}-\beta _{1}q^{8}+\cdots$$
171.3.c.f $4$ $4.659$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$10$$ $$34$$ $$q-\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(3-\beta _{2})q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(171, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(171, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 2}$$