# Properties

 Label 105.4.d Level $105$ Weight $4$ Character orbit 105.d Rep. character $\chi_{105}(64,\cdot)$ Character field $\Q$ Dimension $16$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ 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 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

## Trace form

 $$16q - 60q^{4} - 28q^{5} - 12q^{6} - 144q^{9} + O(q^{10})$$ $$16q - 60q^{4} - 28q^{5} - 12q^{6} - 144q^{9} + 8q^{10} - 24q^{15} + 172q^{16} - 72q^{19} + 700q^{20} - 84q^{21} + 324q^{24} - 8q^{25} + 696q^{26} - 1080q^{29} - 432q^{30} - 48q^{31} - 152q^{34} + 56q^{35} + 540q^{36} + 600q^{39} - 2144q^{40} + 1192q^{41} + 32q^{44} + 252q^{45} - 64q^{46} - 784q^{49} - 1288q^{50} - 1560q^{51} + 108q^{54} + 1408q^{55} + 168q^{56} + 352q^{59} - 228q^{60} - 440q^{61} + 1476q^{64} - 3312q^{65} + 1920q^{66} - 1776q^{69} - 756q^{70} + 904q^{71} + 664q^{74} + 528q^{75} + 7840q^{76} + 4880q^{79} - 332q^{80} + 1296q^{81} + 1008q^{84} - 1272q^{85} - 4200q^{86} + 3304q^{89} - 72q^{90} - 1456q^{91} - 9304q^{94} + 440q^{95} + 1236q^{96} + O(q^{100})$$

## 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.d.a $$6$$ $$6.195$$ 6.0.84052224.1 None $$0$$ $$0$$ $$-14$$ $$0$$ $$q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$$
105.4.d.b $$10$$ $$6.195$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$-14$$ $$0$$ $$q+\beta _{6}q^{2}-3\beta _{2}q^{3}+(-5-\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(105, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(105, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$