# Properties

 Label 10.4.b Level $10$ Weight $4$ Character orbit 10.b Rep. character $\chi_{10}(9,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$10 = 2 \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 10.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(10, [\chi])$$.

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

## Trace form

 $$2 q - 8 q^{4} - 10 q^{5} + 8 q^{6} + 46 q^{9} + O(q^{10})$$ $$2 q - 8 q^{4} - 10 q^{5} + 8 q^{6} + 46 q^{9} + 40 q^{10} - 56 q^{11} - 104 q^{14} - 40 q^{15} + 32 q^{16} + 120 q^{19} + 40 q^{20} + 104 q^{21} - 32 q^{24} - 150 q^{25} + 48 q^{26} - 180 q^{29} - 40 q^{30} - 256 q^{31} + 256 q^{34} + 520 q^{35} - 184 q^{36} - 48 q^{39} - 160 q^{40} + 484 q^{41} + 224 q^{44} - 230 q^{45} - 232 q^{46} - 666 q^{49} - 400 q^{50} - 256 q^{51} + 400 q^{54} + 280 q^{55} + 416 q^{56} + 40 q^{59} + 160 q^{60} + 1084 q^{61} - 128 q^{64} - 240 q^{65} - 224 q^{66} + 232 q^{69} + 520 q^{70} - 2256 q^{71} - 944 q^{74} + 400 q^{75} - 480 q^{76} + 1440 q^{79} - 160 q^{80} + 842 q^{81} - 416 q^{84} - 1280 q^{85} + 1448 q^{86} + 980 q^{89} + 920 q^{90} + 624 q^{91} - 904 q^{94} - 600 q^{95} + 128 q^{96} - 1288 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(10, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.4.b.a $2$ $0.590$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-10$$ $$0$$ $$q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots$$