# Properties

 Label 10.6.b Level $10$ Weight $6$ Character orbit 10.b Rep. character $\chi_{10}(9,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $9$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$10 = 2 \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ 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: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(10, [\chi])$$.

Total New Old
Modular forms 10 2 8
Cusp forms 6 2 4
Eisenstein series 4 0 4

## Trace form

 $$2 q - 32 q^{4} + 110 q^{5} - 112 q^{6} + 94 q^{9} + O(q^{10})$$ $$2 q - 32 q^{4} + 110 q^{5} - 112 q^{6} + 94 q^{9} - 80 q^{10} - 296 q^{11} + 1264 q^{14} - 280 q^{15} + 512 q^{16} - 4440 q^{19} - 1760 q^{20} + 4424 q^{21} + 1792 q^{24} + 5850 q^{25} - 5472 q^{26} + 540 q^{29} - 6160 q^{30} - 4096 q^{31} + 16384 q^{34} + 3160 q^{35} - 1504 q^{36} - 19152 q^{39} + 1280 q^{40} - 4796 q^{41} + 4736 q^{44} + 5170 q^{45} + 9968 q^{46} - 16314 q^{49} - 8800 q^{50} + 57344 q^{51} - 32480 q^{54} - 16280 q^{55} - 20224 q^{56} + 79480 q^{59} + 4480 q^{60} - 84596 q^{61} - 8192 q^{64} - 13680 q^{65} + 16576 q^{66} + 34888 q^{69} + 69520 q^{70} - 8496 q^{71} - 34976 q^{74} - 30800 q^{75} + 71040 q^{76} - 70560 q^{79} + 28160 q^{80} - 90838 q^{81} - 70784 q^{84} + 40960 q^{85} - 18352 q^{86} + 170420 q^{89} - 3760 q^{90} + 216144 q^{91} - 85456 q^{94} - 244200 q^{95} - 28672 q^{96} - 13912 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(10, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.6.b.a $2$ $1.604$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$110$$ $$0$$ $$q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(10, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(10, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 2}$$