# Properties

 Label 105.2.q Level $105$ Weight $2$ Character orbit 105.q Rep. character $\chi_{105}(4,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $32$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 105.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 40 16 24
Cusp forms 24 16 8
Eisenstein series 16 0 16

## Trace form

 $$16q + 8q^{4} + 2q^{5} - 8q^{6} + 8q^{9} + O(q^{10})$$ $$16q + 8q^{4} + 2q^{5} - 8q^{6} + 8q^{9} - 4q^{10} - 24q^{14} - 4q^{15} - 24q^{19} - 8q^{20} - 4q^{21} - 12q^{24} - 4q^{25} - 12q^{26} + 24q^{29} - 12q^{30} + 16q^{31} + 16q^{34} - 10q^{35} + 16q^{36} - 4q^{39} + 32q^{40} + 16q^{41} + 20q^{44} - 2q^{45} - 32q^{46} - 40q^{49} - 40q^{50} + 4q^{51} - 4q^{54} + 8q^{55} + 84q^{56} + 4q^{59} + 16q^{60} + 16q^{61} + 16q^{64} + 30q^{65} + 28q^{66} + 40q^{69} + 16q^{70} - 56q^{71} + 40q^{74} + 8q^{75} - 64q^{76} - 16q^{79} + 52q^{80} - 8q^{81} + 12q^{84} - 64q^{85} - 48q^{86} + 16q^{89} - 8q^{90} + 8q^{91} - 32q^{94} - 22q^{95} + 8q^{96} + O(q^{100})$$

## 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.q.a $$16$$ $$0.838$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\beta _{5}+\beta _{6}-\beta _{15})q^{2}+\beta _{3}q^{3}+(1+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(105, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(105, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$