# Properties

 Label 105.4.g Level $105$ Weight $4$ Character orbit 105.g Rep. character $\chi_{105}(104,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $2$ Sturm bound $64$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 105.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$64$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(105, [\chi])$$.

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

## Trace form

 $$44q + 152q^{4} - 48q^{9} + O(q^{10})$$ $$44q + 152q^{4} - 48q^{9} + 12q^{15} + 440q^{16} - 48q^{21} + 212q^{25} - 336q^{30} - 1104q^{36} - 252q^{39} - 1488q^{46} - 124q^{49} + 1620q^{51} + 384q^{60} - 2008q^{64} - 3000q^{70} - 248q^{79} + 3072q^{81} - 624q^{84} + 208q^{85} + 1864q^{91} + 6396q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
105.4.g.a $$4$$ $$6.195$$ $$\Q(\sqrt{-5}, \sqrt{7})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{1}-\beta _{3})q^{3}-8q^{4}-5\beta _{1}q^{5}+7\beta _{3}q^{7}+\cdots$$
105.4.g.b $$40$$ $$6.195$$ None $$0$$ $$0$$ $$0$$ $$0$$