# Properties

 Label 105.2.g Level $105$ Weight $2$ Character orbit 105.g Rep. character $\chi_{105}(104,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $3$ Sturm bound $32$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 105.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$32$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(105, [\chi])$$.

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

## Trace form

 $$12 q - 6 q^{9} + O(q^{10})$$ $$12 q - 6 q^{9} + 6 q^{15} - 24 q^{16} + 6 q^{21} - 12 q^{25} - 24 q^{30} - 12 q^{36} + 18 q^{39} + 48 q^{46} - 12 q^{49} + 42 q^{51} + 36 q^{60} - 24 q^{64} + 24 q^{70} + 60 q^{79} - 90 q^{81} - 36 q^{84} - 12 q^{85} - 60 q^{91} + 6 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.2.g.a $4$ $0.838$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$-4$$ $$0$$ $$4$$ $$q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
105.2.g.b $4$ $0.838$ $$\Q(\sqrt{-5}, \sqrt{7})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
105.2.g.c $4$ $0.838$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$4$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$