# Properties

 Label 105.3.r Level $105$ Weight $3$ Character orbit 105.r Rep. character $\chi_{105}(19,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(105, [\chi])$$.

Total New Old
Modular forms 72 32 40
Cusp forms 56 32 24
Eisenstein series 16 0 16

## Trace form

 $$32q + 32q^{4} - 6q^{5} - 48q^{9} + O(q^{10})$$ $$32q + 32q^{4} - 6q^{5} - 48q^{9} + 78q^{10} - 28q^{11} + 60q^{14} - 24q^{15} - 40q^{16} - 60q^{19} + 12q^{21} - 34q^{25} - 96q^{26} - 88q^{29} + 84q^{31} - 170q^{35} - 192q^{36} + 36q^{39} + 330q^{40} + 320q^{44} + 18q^{45} - 60q^{46} + 356q^{49} + 12q^{51} - 468q^{56} - 804q^{59} - 198q^{60} + 336q^{61} - 400q^{64} - 46q^{65} - 108q^{66} - 438q^{70} + 344q^{71} + 900q^{74} + 144q^{75} - 20q^{79} + 1140q^{80} - 144q^{81} + 780q^{84} + 304q^{85} + 144q^{86} + 24q^{89} - 224q^{91} - 924q^{94} - 342q^{95} + 900q^{96} + 168q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
105.3.r.a $$32$$ $$2.861$$ None $$0$$ $$0$$ $$-6$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(105, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(105, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$