# Properties

 Label 5.6.b Level $5$ Weight $6$ Character orbit 5.b Rep. character $\chi_{5}(4,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $3$ Trace bound $0$

# Related objects

## Defining parameters

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

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(5, [\chi])$$.

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

## Trace form

 $$2q - 24q^{4} - 90q^{5} + 264q^{6} - 306q^{9} + O(q^{10})$$ $$2q - 24q^{4} - 90q^{5} + 264q^{6} - 306q^{9} - 440q^{10} + 504q^{11} + 792q^{14} + 1320q^{15} - 2528q^{16} - 440q^{19} + 1080q^{20} - 2376q^{21} + 5280q^{24} + 1850q^{25} + 1584q^{26} - 13860q^{29} - 11880q^{30} + 13504q^{31} + 9152q^{34} + 3960q^{35} + 3672q^{36} - 4752q^{39} - 8800q^{40} - 396q^{41} - 6048q^{44} + 13770q^{45} - 32296q^{46} + 26486q^{49} + 39600q^{50} - 27456q^{51} + 23760q^{54} - 22680q^{55} + 15840q^{56} - 49320q^{59} - 15840q^{60} - 11396q^{61} - 25984q^{64} + 7920q^{65} + 66528q^{66} + 96888q^{69} - 35640q^{70} + 106704q^{71} - 185328q^{74} - 118800q^{75} + 5280q^{76} + 103840q^{79} + 113760q^{80} - 145638q^{81} + 28512q^{84} + 45760q^{85} + 5544q^{86} - 19980q^{89} + 67320q^{90} - 14256q^{91} + 139832q^{94} + 19800q^{95} - 164736q^{96} - 77112q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(5, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
5.6.b.a $$2$$ $$0.802$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$-90$$ $$0$$ $$q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots$$