# Properties

 Label 165.2.f Level $165$ Weight $2$ Character orbit 165.f Rep. character $\chi_{165}(131,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $2$ Sturm bound $48$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 165.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

## Trace form

 $$16q - 4q^{3} + 16q^{4} + 8q^{9} + O(q^{10})$$ $$16q - 4q^{3} + 16q^{4} + 8q^{9} - 12q^{12} - 4q^{15} - 16q^{16} - 8q^{22} - 16q^{25} + 20q^{27} + 4q^{33} - 32q^{34} - 24q^{36} + 16q^{37} - 8q^{42} - 52q^{48} - 16q^{49} + 8q^{55} + 8q^{58} + 12q^{60} + 24q^{66} + 88q^{67} - 40q^{69} + 24q^{70} + 4q^{75} + 88q^{78} + 16q^{81} - 56q^{82} + 16q^{88} + 16q^{91} - 56q^{93} - 48q^{97} + 56q^{99} + O(q^{100})$$

## 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.f.a $$8$$ $$1.318$$ 8.0.619810816.2 None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-\beta _{3}-\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots$$
165.2.f.b $$8$$ $$1.318$$ 8.0.619810816.2 None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$$

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

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