# Properties

 Label 165.2.m Level $165$ Weight $2$ Character orbit 165.m Rep. character $\chi_{165}(16,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $32$ Newform subspaces $4$ Sturm bound $48$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 165.m (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(165, [\chi])$$.

Total New Old
Modular forms 112 32 80
Cusp forms 80 32 48
Eisenstein series 32 0 32

## Trace form

 $$32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} - 8 q^{9} + O(q^{10})$$ $$32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 4 q^{13} - 16 q^{16} - 16 q^{17} - 12 q^{18} + 8 q^{19} + 8 q^{20} - 32 q^{22} - 8 q^{23} - 36 q^{24} - 8 q^{25} + 24 q^{26} + 28 q^{28} + 8 q^{29} + 4 q^{30} + 12 q^{31} + 56 q^{32} + 4 q^{33} + 8 q^{34} + 8 q^{35} - 52 q^{37} - 36 q^{38} + 8 q^{39} + 12 q^{40} - 28 q^{41} + 32 q^{42} - 40 q^{43} + 52 q^{44} + 24 q^{46} - 32 q^{47} + 32 q^{48} - 4 q^{49} + 8 q^{50} - 4 q^{51} + 52 q^{52} + 16 q^{53} - 12 q^{55} + 8 q^{57} - 20 q^{58} + 64 q^{59} + 20 q^{61} + 16 q^{62} + 8 q^{63} - 28 q^{64} + 24 q^{65} + 20 q^{66} - 8 q^{67} - 40 q^{68} + 16 q^{69} - 28 q^{70} + 24 q^{71} + 4 q^{72} - 36 q^{73} - 84 q^{74} - 40 q^{76} - 92 q^{77} + 64 q^{78} - 32 q^{79} + 16 q^{80} - 8 q^{81} - 36 q^{82} - 4 q^{83} - 48 q^{84} + 8 q^{85} - 56 q^{86} - 88 q^{87} + 20 q^{88} - 32 q^{89} + 4 q^{90} - 12 q^{91} - 80 q^{92} + 32 q^{93} - 36 q^{94} - 12 q^{96} + 60 q^{97} + 96 q^{98} - 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(165, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.2.m.a $8$ $1.318$ 8.0.13140625.1 None $$0$$ $$-2$$ $$2$$ $$1$$ $$q+(1-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6})q^{2}+(-1+\cdots)q^{3}+\cdots$$
165.2.m.b $8$ $1.318$ 8.0.819390625.1 None $$2$$ $$2$$ $$2$$ $$9$$ $$q+\beta _{4}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
165.2.m.c $8$ $1.318$ $$\Q(\zeta_{15})$$ None $$2$$ $$2$$ $$-2$$ $$-5$$ $$q+(-1+2\zeta_{15}-\zeta_{15}^{3}+\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots$$
165.2.m.d $8$ $1.318$ 8.0.13140625.1 None $$4$$ $$-2$$ $$-2$$ $$3$$ $$q+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(165, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(165, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$