# Properties

 Label 165.3.l Level $165$ Weight $3$ Character orbit 165.l Rep. character $\chi_{165}(32,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $88$ Newform subspaces $7$ Sturm bound $72$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 165.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$165$$ Character field: $$\Q(i)$$ Newform subspaces: $$7$$ Sturm bound: $$72$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$2$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(165, [\chi])$$.

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

## Trace form

 $$88 q - 6 q^{3} + O(q^{10})$$ $$88 q - 6 q^{3} - 36 q^{15} - 272 q^{16} + 52 q^{22} - 84 q^{25} + 60 q^{27} + 16 q^{31} - 22 q^{33} + 408 q^{36} - 220 q^{37} + 152 q^{42} - 232 q^{45} - 24 q^{48} + 96 q^{55} + 272 q^{58} + 256 q^{60} + 324 q^{67} - 240 q^{70} + 156 q^{75} + 688 q^{78} - 540 q^{81} + 104 q^{82} - 556 q^{88} - 688 q^{91} - 710 q^{93} - 124 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(165, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.3.l.a $4$ $4.496$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$-12$$ $$-16$$ $$0$$ $$q+\beta _{1}q^{2}-3q^{3}+\beta _{2}q^{4}+(-4-3\beta _{2}+\cdots)q^{5}+\cdots$$
165.3.l.b $4$ $4.496$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-3\beta _{2}q^{3}-\beta _{2}q^{4}+5\beta _{2}q^{5}+\cdots$$
165.3.l.c $4$ $4.496$ $$\Q(i, \sqrt{11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-3\beta _{2})q^{3}-4\beta _{2}q^{4}+(3\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$$
165.3.l.d $4$ $4.496$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$16$$ $$0$$ $$q+\beta _{1}q^{2}+3\beta _{2}q^{3}+\beta _{2}q^{4}+(4+3\beta _{2}+\cdots)q^{5}+\cdots$$
165.3.l.e $4$ $4.496$ $$\Q(i, \sqrt{11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$10$$ $$0$$ $$0$$ $$q+(3+\beta _{3})q^{3}+4\beta _{2}q^{4}+(-3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
165.3.l.f $4$ $4.496$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$12$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+3q^{3}-\beta _{2}q^{4}-5\beta _{2}q^{5}+\cdots$$
165.3.l.g $64$ $4.496$ None $$0$$ $$-16$$ $$0$$ $$0$$