# Properties

 Label 66.2.b Level $66$ Weight $2$ Character orbit 66.b Rep. character $\chi_{66}(65,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $24$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$66 = 2 \cdot 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 66.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(66, [\chi])$$.

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

## Trace form

 $$4 q - 4 q^{3} + 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$4 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{12} - 8 q^{15} + 4 q^{16} - 12 q^{22} + 12 q^{25} + 20 q^{27} - 16 q^{31} + 8 q^{33} - 4 q^{36} + 8 q^{37} + 24 q^{42} + 16 q^{45} - 4 q^{48} - 44 q^{49} + 8 q^{55} - 24 q^{58} - 8 q^{60} + 4 q^{64} + 12 q^{66} - 16 q^{67} - 8 q^{69} + 24 q^{70} - 12 q^{75} - 24 q^{78} - 28 q^{81} + 24 q^{82} - 12 q^{88} + 72 q^{91} + 16 q^{93} + 32 q^{97} - 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(66, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
66.2.b.a $2$ $0.527$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$-2$$ $$0$$ $$0$$ $$q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots$$
66.2.b.b $2$ $0.527$ $$\Q(\sqrt{-2})$$ None $$2$$ $$-2$$ $$0$$ $$0$$ $$q+q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(66, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(66, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$